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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Tate module; Galois representation; analogue of Falting's semi-simplicity theorem; Shafarevich-type finiteness result; isogenies of Drinfel'd modules; heights \textsc{R.~Dedekind}\textsc{and}\textsc{H.~Weber}, Theorie der algebraischen Functionen einer Veränderlichen, J. Reine Angew. Math. \textbf{92} (1882), 181-290.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Weil canonical height; complex dynamics; regular polynomial endomorphisms; fibral families; Green's functions
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Manin's conjecture; rational points; bounded height; tri-linear form; tri-projective space; circle method; asymptotic formula; geometry of numbers Mignot, T, Points de hauteur bornée sur LES hypersurfaces lisses de l'espace triprojectif, Int. J. Number Theory, 11, 945-995, (2015)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. canonical heights; dynamical degree; multiplicative groups; preperiodic points; effective lower bounds; Baker's theorem
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Manin's conjecture; rational points; heights; automorphic representation theory
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Lehmer conjecture; small points; height; Zilber-Pink conjecture Carrizosa, M.: Petits points et multiplication complexe. Int. Math. Res. Not. \textbf{16}, 3016-3097 (2009)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. curve; function field; Jacobian; abelian variety; finite field; Mordell-Weil group; torsion; rank; \(L\)-function; Birch and Swinnerton-Dyer conjecture; Tate-Shafarevich group; Tamagawa number; endomorphism algebra; descent; height; Néron model; Kodaira-Spencer map; monodromy
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. hypergeometric groups; \(K3\) surfaces; automorphisms; entropy; unimodular lattices; Salem numbers; Lehmer's number; Siegel disks
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Gauss-Manin connection; Bombieri-Dwork conjecture; arithmetic results; values of G-functions at algebraic points; applications of G-function theory; geometric differential equations; Fuchsian differential systems; heights; linear independence; global relations; Grothendieck's conjecture; algebraic relations between periods of algebraic varieties; bound for the heights of certain abelian varieties with a large endomorphism ring; transcendence André, Y.: G-functions and Geometry, Aspects of Mathematics, vol. E13. Friedr. Vieweg & Sohn, Braunschweig (1989)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. abelian varieties; finite fields; genus 3; class field theory; curves; rational points; genus 2; Deligne-Lusztig curves; ; Smyth's method; Voloch bound; Ihara constant; Ihara's tower theorem; Golod-Shafarevich theorem; Oesterle's theorem; asymptotic result; explicit formulas Weil's bound
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. strong Weil curve; Manin constant; Néron model functor; Manin's conjecture; semi-stable elliptic curves Abbes, Ahmed; Ullmo, Emmanuel, À propos de la conjecture de Manin pour les courbes elliptiques modulaires, Compositio Math., 103, 3, 269-286, (1996)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Bloch-Beilinson filtration; Bloch's conjecture; Chow groups; (double) EPW cubes; hyperkähler varieties; \(K3\) surfaces; motives; multiplicative Chow-Künneth decomposition; non-symplectic involution; splitting property
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. transcendence; exponential function; Drinfeld module; lattice; analog of Siegel's lemma; Hilbert's 7th problem Yu, J.: Transcendence theory over function fields. Duke math. J. 52, 517-527 (1985)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Shimura-Taniyama-Weil conjecture; semistable elliptic curves; Fermat's last theorem; Birch and Swinnerton-Dyer conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. geometric Bogomolov conjecture; Bogomolov conjecture; canonical heights; canonical measures; small points
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Kolyvagin's descent; Mordell-Weil groups; modular elliptic curve; ring class field extension; Heegner point; Birch and Swinnerton-Dyer conjecture Bertolini, M. and Darmon, H. : Kolyvagin's descent and Mordell-Weil groups over ring class fields , J. für die Reine und Angewandte Mathematik 412 (1990), 63-74.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Arakelov theory; Weil height; Del Pezzo surface; linear growth conjecture Yu. I. Manin, et\! \lccYu. Tschinkel, Points of bounded height on del Pezzo surfaces , Compositio Math. 85 (1993), 315--332.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Taniyama-Weil conjecture; \(L\)-functions; motivic \(L\)-functions; automorphic \(L\)-functions; Fermat's last theorem; arithmetic study of elliptic curves; modular forms A. Knapp, \textit{Elliptic Curves}, Princeton Univ. Press, Princeton, New Jersey (1992).
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. diophantine geometry; arithmetic algebraic geometry; Mordell conjecture; arithmetic Nevanlinna theory; Taniyama-Shimura-Weil conjecture; Heegner points; Arakelov theory; heights; diophantine approximation; Hasse principle; minimal isogenies between 1-motives; integral points; Birch-Swinnerton-Dyer conjecture Lang, S.: Survey of Diophantine geometry. (1997)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. dynamical Mordell-Lang conjecture; Weil height; algebraic points; étale maps
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. multilinear algebra; tensor products; algebraic varieties; secant varieties; representation theory; complexity theory; matrices; monograph; textbook; matrix multiplication; tensor decomposition; tensor network; border rank; tensor calculus; projective algebraic geometry; Terracini's Lemma; polynomial Waring problem; Segre varieties; signal processing; Littlewood-Richardson rule; Pieri's formula; Strassen's equation; Young flattening; Friedland's equation; Fano varieties of line; Chow varieties of zero cycle; Brill's equation; normal form; Konstant's theorem; Bott-Borel-Weil theorem; Koszul sequences; syzygies J. M. Landsberg, \textit{Tensors: Geometry and Applications}, American Mathematical Society, Providence, RI, 2012.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. canonical local heights; Julia set; pre-periodic point; Weil height; non-archimedean places G. S. Call and S.W. Goldstine, ''Canonical heights on projective space,'' J. Number Theory 63(2), 211--243 (1997).
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. height functions; Jacobian surfaces; Jacobian variety of a hyperelliptic curve; Néron's local pairing; canonical local height at archimedean places; Birch and Swinnerton-Dyer conjecture Yoshitomi K.: On height functions on Jacobian surfaces. Manuscripta Math. 96, 37--66 (1998)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. heights; Lehmer conjecture; algebraic numbers; free abelian groups
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. wild ramification; Galois cover; Abhyankar's inertia conjecture; Abhyankar's lemma Kumar, Manish: Killing wild ramification, Isr. J. Math. (2013)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Galois representations; modular forms; Fermat's last theorem; Taniyama- Weil conjecture J.-P. Serre, Lettre à J.-F. Mestre , Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985) ed. K. Ribet, Contemp. Math., vol. 67, Amer. Math. Soc., Providence, RI, 1987, pp. 263-268.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow group; motive; Bloch-Beilinson filtration; Beauville's ``splitting property'' conjecture; multiplicative Chow-Künneth decomposition; Fano threefolds; tautological ring
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. ABC conjecture; the error term in the ABC conjecture; radicalized Vojta height inequality; Diophantine approximation; Roth's theorem; type of an algebraic number; Mordell's conjecture; effective Mordell van Frankenhuijsen, Machiel, \(ABC\) implies the radicalized Vojta height inequality for curves, J. Number Theory, 127, 2, 292-300, (2007)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. multiplicative group; algebraic curves; height functions; finiteness result; rational points P. Habegger, A Bogomolov property for curves modulo algebraic subgroups , Bull. Soc. Math. France 137 (2009), 93--125.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Mordell-Weil groups of elliptic curves with complex; multiplication; Weil parametrizations; L-function attached to a Weil curve; anti-cyclotomic tower; Iwasawa theory of elliptic curves; p-adic height pairing; p-adic L-functions; p-adic Heegner measures; finiteness of the Tate-Shafarevich group; Mordell-Weil groups of elliptic curves with complex multiplication B. Mazur, Modular curves and arithmetic, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 185 -- 211.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Siegel modular forms; Kudla's conjecture; Siegel operator M. Westerholt-Raum, \textit{Indefinite theta series on tetrahedral cones}, arXiv:1608.08874.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Kronecker's Jugendtraum; elliptic functions; elliptic integrals; arithmetic of elliptic curves; Weierstrass \(\wp\)-function; projective plane cubics; Abel's theorem; inversion problem; Jacobi functions; theta functions; Lefschetz theorem; embeddings; theta identities; Euler identities; Jacobi substitutions; quadratic reciprocity; Siegel modular group; modular forms; Eisenstein series; modular equation; arithmetic subgroups; arithmetic applications; solvability of algebraic equations; Galois theory; Klein's icosaeder; quintic equation; imaginary quadratic number fields; class invariants; class polynomial; Mordell-Weil theorem Henry McKean and Victor Moll, \textit{Elliptic Curves}, Cambridge University Press, Cambridge, 1997.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Lehmer conjecture for an elliptic curve; Néron-Tate height M. Hindry, J.H. Silverman, On Lehmer's conjecture for elliptic curves, in Séminaire de Théorie des Nombres, Paris (1988--1989), Progress in Mathematics, Vol. 91, Birkhäuser, Boston, MA, 1990, pp. 103--116.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. lower bound; Faltings height; period lattice; Masser's matrix lemma P. Autissier, Un lemme matriciel effectif , Math. Z. 273 (2013), 355-361.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Tate conjecture; Zarhin's trick; Barsotti-Tate groups; heights of cycles Bost, Jean-Benoît; Freixas i Montplet, Gerard, Semi-abelian schemes and heights of cycles in moduli spaces of abelian varieties, Rend. Semin. Mat. Univ. Padova, 128, 55-89 (2013), (2012)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Lehmer's problem; Coxeter link; fibered link; Mahler measure; McKay's correspondence
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. heights; Batyrev-Manin conjecture; adelic height; adelic metric; rational points; Northcott property; Peyre constant Le Rudulier, C.: Points algébriques de hauteur bornée sur la droite projective. J. théor. Nombres Bordeaux 26, No. 3 (2014)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. elliptic surfaces; elliptic curves; Nagao's conjecture; Mordell-Weil rank
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. height inequality; integral points; greatest common divisors; blowups; Schmidt subspace theorem; Vojta's conjecture; entire curves
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Noetherian functions; non-Archimedean geometry; Pfaffian functions; rational points of bounded height; Wilkie's conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. rationality questions; rational points; Hasse-Weil \(L\)-function of modular elliptic curves; local-global principles; Selmer's curve; smooth projective varieties; Tate-Shafarevich group; Tate-Shafarevich conjecture; Selmer groups of elliptic curves; class field theory; Kolyvagin test classes Mazur B.: On the passage from local to global in number theory. Bull. Amer. Math. Soc. (N.S.) 29(1), 14--50 (1993)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow groups; motives; Bloch's conjecture; Bloch-Beilinson filtration; hyperkähler varieties; multiplicative Chow-Künneth decomposition; splitting property; finite-dimensional motive
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Weil conjectures; Mordell's conjecture; Fermat's Last Theorem
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. iteration of rational maps; integral point; dynamical system; \(\varphi\)- canonical heights; diophantine properties of orbits; orbit; diophantine equations; Thue equations; Siegel's theorem Silverman J.H.: Integer points, Diophantine approximation, and iteration of rational maps. Duke Math. J. 71(3), 793--829 (1993)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. height zeta function; rational points; equivariant compactification; Fourier analysis; Manin's conjecture ____, Points of bounded height on equivariant compactifications of vector groups, II . J. Number Theory 85 ( 2000 ), n^\circ 2 , 172 - 188 . MR 1802710 | Zbl 0963.11034
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Euler product; arithmetic surface; Jacobian zeta function; modular curve; survey; Dirichlet series; L-series of elliptic curves; conjecture of Birch and Swinnerton-Dyer; Hasse-Weil conjecture; analytic continuation; functional equation; Shimura-Taniyama conjecture; Serre's conjecture; modular representations
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Fermat's last theorem; Diophantine equations; elliptic functions; elliptic curves; modular functions; Galois theory; representation theory; Weil-Shimura-Taniyama conjecture; abc conjecture; Serre conjectures; Mordell-Weil theorem Hellegouarch, Y.: Invitation to the Mathematics of Fermat-Wiles. Academic Press, Cambridge (2002)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Jacobian; genus four curves; universal family; Mordell-Weil group; Franchetta's conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. heights of abelian varieties; Néron-Tate height; degree of projective varieties; local height; Arakelov theory; Wirtinger theorem; Chow form; Mahler measure Philippon, P.; Sur des hauteurs alternatives. I; Math. Ann.: 1991; Volume 289 ,255-284.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. conic; rational points; Manin's conjecture; height; uniform; explicit; quadric; parameterization; norm; error term Sofos, E.: Rational points on the Fermat cubic surface, (2014)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. del Pezzo surfaces; rational points; height; Manin's conjecture U. Derenthal and D. Loughran, Singular del Pezzo surfaces that are equivariant compactifications, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 377 (2010), no. Issledovaniya po Teorii Chisel. 10, 26 -- 43, 241 (English, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 171 (2010), no. 6, 714 -- 724.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. height; zeta function; rational points; Manin's conjecture; Diophantine equations; cubic surfaces
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. moving hypersurfaces; Schmidt's subspace theorem; local ring; Weil height Chen, Z.; Ru, M.; Yan, Q., Schmidt's subspace theorem with moving targets, Int. Math. Res. Not. IMRN, 15, 6305-6329, (2015)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Ribet's theorem; Fermat's last theorem; irreducible representation; Shimura-Taniyama-Weil conjecture; semi-stable elliptic curves Prasad, D.: Ribet's theorem: Shimura-Taniyama-Weil implies Fermat. In: Seminar on Fermat's Last Theorem (Toronto, ON, 1993--1994). CMS Conf. Proc., vol. 17, pp. 155--177. Providence, RI: Amer. Math. Soc. 1995
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. abelian varieties; global fields; function fields; \(L\)-function; Birch and Swinnerton-Dyer conjecture; heights; torsion points; Néron models; Brauer-Siegel theorem Hindry, M.; Pacheco, A., An analogue of the Brauer-Siegel theorem for abelian varieties in positive characteristic, Mosc. Math. J., 16, 1, 45-93, (2016)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Lehmer's problem in dimension two; lower bound for height of non-torsion point Pontreau, C.: Minoration effective de la hauteur des points d'une courbe de gm2 définie sur Q. Acta arith. 120, No. 1, 1-26 (2005)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Vojta's conjecture; heights; rational points; elliptic curves McKinnon D.: Vojta's main conjecture for blowup surfaces. Proc. Am. Math. Soc. 131(1), 1--12 (2003) (electronic)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. conjecture of Birch and Swinnerton-Dyer; Weil curves; p-adic height D. Bernardi and C. Goldstein, Variante \(p\)-adique de la conjecture de Birch et Swinnerton-Dyer , C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 10, 455-458.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Manin-Mumford conjecture; Lehmer problem; normalised height; Diophantine approximation Ratazzi N., Intersection de courbes et de sous-groupes, et problèmes de minoration de hauteur dans les variétés abéliennes C.M. À paraître aux Annales de l'Institut Fourier.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Hecke quantum unique ergodicity rate conjecture; Hannay-Berry model of quantum mechanics on the two-dimensional torus; arithmetic quantum chaos; canonical model; Deligne's letter; geometric Weil representation; Weil representation
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Weil pairing; elliptic curve with complex multiplication; \(p\)-adic Néron-Tate height; Birch--Swinnerton-Dyer conjecture; \(p\)-adic \(L\)-series Perrin-Riou, Descente infinie et hauteur p-adique sur les courbes elliptiques á multiplication complexe, Invent. Math. 70 pp 369-- (1982)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. cubic surface; rational points; height; counting function; Manin's conjecture; smallest point; Peyre constant; numerical computation Elsenhans, A. -S.; Jahnel, J.: Experiments with general cubic surfaces, Progr. math. 269, 637-654 (2007)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. equidistribution theorem; Arakelov geometry; arithmetic height functions; Northcott's theorem; Bogomolov's conjecture; Néron-Tate height; Raynaud's theorem; Abelian variety; canonical height function A. Moriwaki, Arithmetic height functions over finitely generated fields, Invent. Math. 140 (2000), 101-142.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. covolume of the relation group; Lehmer's conjecture; lattices; duality; abelian variety [5]D. Bertrand, Duality on tori and multiplicative dependence relations, J. Austral. Math. Soc. Ser. A 62 (1997), 198--216.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Fano orbifolds; rational points; heights; Manin's conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. inter-universal Teichmüller theory; punctured elliptic curve; number field; mono-complex; étale theta function; 6-torsion points; height; explicit estimate; effective version; diophantine inequality; ABC conjecture; Szpiro conjecture; Fermat's last theorem
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. identity between Faltings height of CM abelian variety and logarithmic derivative of Artin \(L\)-functions; elliptic modular form; arithmetic intersection; Siegel modular forms; Hilbert modular forms; Colmez conjecture Yang, T., \textit{the chowla-Selberg formula and the Colmez conjecture}, Canad. J. Math., 62, 456-472, (2010)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Mordell-Weil rank; elliptic surface; elliptic curve; Tate's conjecture Silverman, J.: A bound for the Mordell-Weil rank of an elliptic curve after a cyclic base extension. J. Alg. Geom. 9, 301--308 (2000)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Vojta's conjecture; hyperbolicity; heights; general type; rational points; moduli spaces
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Fermat's last theorem; Shimura-Taniyama-Weil conjecture; elliptic curves; modular forms; Galois representations Fernando Q. Gouvêa, ''A marvelous proof'', Amer. Math. Monthly 101 (1994), no. 3, 203 -- 222.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. exponential height; diophantine equations; Bogomolov-Miyaoka-Yau inequality; arithmetic surface; Arakelov's intersection theory; intersection numbers; Szpiro conjecture; Parshin trick; asymptotic Fermat theorem; boundedness of the torsion of elliptic curves A. N. Parshin, ``The Bogomolov -- Miyaoka -- Yau inequality for the arithmetical surfaces and its applications'', Seḿinaire de theórie des nombres (Paris, 1986 -- 87), Progr. Math., 75, Birkhaüser, Boston, MA, 1988, 299 -- 312
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Weierstraß \(\wp\)-function; Mordell's theorem; Hasse's theorem; \(L\)- function; Birch and Swinnerton-Dyer conjecture; \(j\)-invariant; rational points of elliptic curves; imaginary quadratic fields; Taniyama-Weil conjecture Henri Cohen, Elliptic curves, From number theory to physics (Les Houches, 1989) Springer, Berlin, 1992, pp. 212 -- 237.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Szpiro's small points conjecture; Arakelov theory; arithmetic surfaces; logarithmic forms; Belyi map; cyclic cover; Néron-Tate height Javanpeykar, A; Känel, R, Szpiro's small points conjecture for cyclic covers, Doc. Math., 19, 1085-1103, (2014)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. normalized height; torus; Abelian extensions; Lehmer's problem Delsinne, Le problème de Lehmer relatif en dimension supérieure, Ann. Sci. École Norm. Sup. 42 6 pp 981-- (2009)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Mordell-Faltings theorem; rational points; Mordell's conjecture; function field; Thue-Siegel-Dyson-Gel'fond theorem Vojta, P., Siegel's theorem in the compact case, \textit{Ann. Math.}, 133, 3, 509-548, (1991)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Fermat last theorem; survey; Fermat's equation; elliptic curve; conjecture of Szpiro; abc-conjecture; Serre's conjecture; existence of a cusp form of weight 2 for \(\Gamma _ 0(2)\); Taniyama-Weil conjecture; theorems of Mazur and Ribet; modular representation Oesterlé ( J. ) .- Nouvelles approches du ''théorème'' de Fermat , Séminaire Bourbaki n^\circ 694 (1987-88). Astérisque 161 -162, 165 - 186 ( 1988 ) Numdam | MR 992208 | Zbl 0668.10024
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Taniyama-Shimura-Weil conjecture; Fermat's conjecture; G. Frey's elliptic curve; reduction at the prime two Kenneth A. Ribet, From the Taniyama-Shimura conjecture to Fermat's last theorem, Ann. Fac. Sci. Toulouse Math. (5) 11 (1990), no. 1, 116 -- 139 (English, with English and French summaries).
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic points; subvarieties; canonical height; nontrivial translates; torsion points; Lehmer's problem; points of minimal height E. Bombieri and U. Zannier, Algebraic points on subvarieties of \?\(^{n}\)_{\?}, Internat. Math. Res. Notices 7 (1995), 333 -- 347.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Manin's conjecture; global field of positive characteristic; projective plane; blowing-up universal torsor; Cox ring; heights ---, Comptage de courbes sur le plan projectif éclaté en trois points alignés, Ann. Inst. Fourier (Grenoble) 59 (2009), 1847-1895.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. toric varieties; Manin's conjecture; distribution of rational points; all the heights
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. arithmetical dynamical system; canonical height; division group; division point; Erdős-Turán Theorem; integral point; Koksma's inequality; linear forms in logarithms; logarithmic equidistribution; multiplicative group; Weyl sums
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Weil transitivity theorem; super-Weil algebra; Grassmann algebra; Yoneda's lemma; Weil-Berezin functor; local functor of points; Schwarz embedding Balduzzi, L; Carmeli, C; Fioresi, R, The local functors of points of supermanifolds, Expo. Math., 28, 201-217, (2010)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow group; motive; Bloch-Beilinson filtration; Beauville's ``splitting property'' conjecture; multiplicative Chow-Künneth decomposition; Fano varieties; tautological ring
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Vojta's conjecture; rational surfaces; integral points; blowups; multiplicative groups; greatest common divisors; Farey sequences Y. Yasufuku, Integral points and Vojta's conjecture on rational surfaces, Trans. Amer. Math. Soc. 364 (2012), no. 2, 767-784.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Jacobian conjecture; Segre's lemma; polynomial mapping; tame generator conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. heights; Poisson formula; Manin's conjecture; Tamagawa measure Antoine Chambert-Loir & Yuri Tschinkel, ``Igusa integrals and volume asymptotics in analytic and adelic geometry'', Confluentes Math.2 (2010) no. 3, p. 351-429
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Shafarevich conjecture; abelian scheme; Falting's height; Jacobian; conductor; abelian schemes of product \(\mathrm{GL}_2\)-type
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic variety; rational points; bounded height; counting function; Manin's conjecture; determinant method; circle method; del Pezzo surfaces Browning, T. D., Quantitative Arithmetic of Projective Varieties, (2009), Birkhäuser, Basel
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. modularity of curves; Shimura curves; Jacobians; Fermat's last theorem; conjecture of Serre; modular Galois representation; Taniyama-Shimura-Weil conjecture Ribet, K. A., On modular representations of Gal(\(\overline{\mbox{{\mathbf Q}}}\)/\textbf{Q}) arising from modular forms, Invent. Math., 100, 431-476, (1990)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. abelian varieties; heights; global fields; Brauer-Siegel theorem; Birch and Swinnerton-Dyer conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Diophantine approximation; rational points on algebraic varieties; arithmetic algebraic geometry; Roth's theorem; nonvanishing lemma for polynomials in several variables; Roth's lemma; Dyson's lemma; Mordell conjecture; Faltings' theorem; finiteness of rational points; algebraic curve of genus greater than one; Vojta's generalization of Dyson's lemma; products of curves of arbitrary genus; Lang conjecture; Subspace Theorem; lower bound for the rational approximation to a hyperplane
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Beilinson conjecture; Grothendieck's standard conjectures of Lefschetz type; Arakelov Chow groups; filtrations on the arithmetic Chow groups; hard Lefschetz conjecture; regulator maps; cubical height of divisors Künnemann, K. : Arakelov Chow groups of abelian schemes, arithmetic Fourier transform and analogues of the standard conjectures of Lefschetz type . Math. Ann. 300 (1994), 365-392.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. elliptic Lehmer problem; elliptic curves; Masser's counting theorem; heights [GM17]A. Galateau and V. Mahé, Some consequences of Masser's counting theorem on elliptic curves, Math. Z. 285 (2017), 613--629.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow group; motive; Bloch-Beilinson filtration; surface of general type; \(K3\) surface; Beauville's ``splitting property'' conjecture; multiplicative Chow-Künneth decomposition
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Weil height machine; ample divisors; effective divisors; intersection theory Dinh, T.-C., Sibony, N.: Density of positive currents and dynamica of Hénon type automorphism of \(\mathbb{C}^k\). Preprint arXiv:1203.5810 (2012)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. abelian varieties; Lehmer's problem; Néron-Tate height; complex multiplication; rational points; number fields; zero estimates David, S; Hindry, M, Minoration de la hauteur de Néron-Tate sur LES variétés abéliennes de type C.M, J. Reine Angew. Math., 529, 1-74, (2000)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Thue equation; Thomas's conjecture; Siegel's theorem; integral points Lettl, G, Parametrized solutions of Diophantine equations, Math. Slovaca, 54, 465-471, (2004)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. linear forms in logarithms; commutative algebraic group; rational case; periodic case; Baker's method; Hermitian vector bundles; Siegel's lemma; \(p\)-adic interpolation
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Séminaire; Pinceaux arithmétiques; Mordell conjecture; modular height; effectiveness of bound for Mordell conjecture; proof of the Mordell conjecture; modular heights; isogenies; Tate conjecture; Shafarevich conjecture; intersection theory of Arakelov Szpiro, L. : Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell , Astérisque 127, Soc. Math. de France (1985).
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. abc-conjecture; Zsigmondy sets; Ih's conjecture; arithmetic dynamics; height theory; arboreal Galois representations; unicritical polynomials
| 0 |
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