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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. Colmez conjecture; Siegel zero; Faltings height; CM abelian varieties; Artin \(L\)-function; good reduction of abelian varieties
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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; non-symplectic involution; multiplicative Chow-Künneth decomposition; splitting property; Calabi-Yau varieties
| 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. singular cubics; isogenies; torsion points; elliptic curves over finite fields; elliptic curves over local fields; Selmer groups; duality; rational torsion; heights; complex multiplication; integral points; Galois representations; survey; group law; endomorphism ring; Weil pairing; elliptic functions; formal group; Shafarevich-Tate groups; \(L\)-series; Tate curves; descent; conjecture of Birch and Swinnerton-Dyer Silverman, J. H.: A survey of the arithmetic theory of elliptic curves. Modular forms and Fermat's last theorem (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. algebraic cycles; Chow groups; motives; Bloch's conjecture; Bloch-Beilinson filtration; hyperkähler varieties; \(K3\) surfaces; Hilbert schemes; non-symplectic involution; multiplicative Chow-Künneth decomposition; ``spread'' of algebraic cycles in a family
| 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 conjecture; product theorem; Roth's lemma; diophantine approximation 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. Weil curve; Galois representation; modular elliptic curve; Hecke cusp form; Serre's conjecture
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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. 0-cycles; vanishing of local factors; metaplectic Eisenstein series of genus 2; derivatives; Siegel-Eisenstein series; global height pairing; algebraic cycles; Shimura curves; local height pairings; Siegel-Weil formula; nonsingular Fourier coefficients Kudla, S., \textit{central derivatives of Eisenstein series and height pairings}, Ann. of Math. (2), 146, 545-646, (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. rational points; universal torsors; height zeta-functin; Manin's conjecture; Campana's program; del Pezzo surface; \(K3\) surface Y. Tschinkel. Algebraic varieties with many rational points. \textit{Arithmetic Geometry}. Clay Math. Proc., Vol. 8. American Mathematical Society, Providence (2009), pp. 243-334.
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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. functional equation for L-function; derivative of L-function; Birch and Swinnerton-Dyer conjecture; Iwasawa L-functions for abelian varieties with multiplicative reductions; p-adic height pairing John W. Jones, Iwasawa \?-functions for multiplicative abelian varieties, Duke Math. J. 59 (1989), no. 2, 399 -- 420.
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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. representation number; Heegner divisor; Shimura curve; Siegel-Weil formula; Kudla's matching principle
| 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 variety; Siegel modular variety; isogeny; Faltings height; canonical height; polyhedral reduction theory; Silverman's specialization 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. linear forms in logarithms; simultaneous approximations; Baker's method; Hirata's reduction; Chudnovsky's process of variable change; adelic slope; Hermitian vector bundle; auxiliary section method; absolute Siegel's lemma; small values Siegel's lemma Gaudron, É., Minorations simultanées de formes linéaires de logarithmes de nombres algébriques, Bull. Soc. Math. France, 142, 1-62, (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. algebraic cycles; Chow groups; motives; Bloch's conjecture; Bloch-Beilinson filtration; hyperkähler varieties; Fano varieties of lines on cubic fourfolds; 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. unique factorization; congruence; quadratic reciprocity; quadratic Gauss sums; Jacobi sums; cubic and biquadratic reciprocity; equations over finite fields; zeta functions; quadratic and cyclotomic fields; Stickelberger relation; Eisenstein reciprocity law; Bernoulli numbers; Dirichlet L-functions; Mordell-Weil theorem for elliptic curves; Mordell conjecture; Taniyama-Weil conjecture; Fermat's last theorem; Birch- Swinnerton-Dyer conjecture; Gauss' class number conjecture K. Ireland and M. Rosen, \textit{A Classical Introduction to Modern Number Theory}, (2nd ed.), Springer, 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. algebraic cycles; Chow groups; motives; Bloch's conjecture; Bloch-Beilinson filtration; hyperkähler varieties; $K3$ surfaces; Hilbert schemes; Calabi-Yau varieties; non-symplectic automorphisms; multiplicative Chow-Künneth decomposition; splitting property; Beauville-Voisin conjecture; 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. Manin's conjecture; points of bounded height; rational points; circle method; toric variety; hypersurface Mignot, T, Points de hauteur bornée sur LES hypersurfaces lisses des variétés toriques, Acta Arith., 172, 1-97, (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. Galois representation; Serre's conjecture; Hecke cusp form; minimal representation; companion representations; Weil curve
| 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; Abhyankar's two point lemma
| 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; curves and their jacobians; Diophantine geometiy; Faltings' theorem; height functions on algebraic varieties; Roth's Lemma; Vojta's inequality
| 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. Mahler's measure; height; arithmetic Hilbert functions; Szegö formula
| 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; thin sets; height functions; circle method; geometry of numbers; biprojective hypersurfaces
| 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. wonderful varieties; adelic points; Manin's conjecture; symmetric spaces; adelic mixing; unipotent flows; ergodic measures Le Rudulier, C: Points algébriques de hauteur bornée sur une surface. available at http://cecile.lerudulier.fr/Articles/surfaces.pdf (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. Hasse-Weil zeta-functions; \(p\)-adic periods; \(p\)-adic fields; \(p\)-adic zeta functions; arithmetic of special values; zeta-functions; generalized Iwasawa main conjecture; Fontain's ring; explicit reciprocity laws; Lubin-Tate formal groups; dual exponential maps Kato, K.: Lectures on the approach to Iwasawa theory for Hasse-Weil \(L\)-functions via \(B_{\mathrm dR}\) II. Non publié
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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. Tamagawa numbers; Weil's Conjecture; moduli stack
| 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; degree 4; singular; asymptotic formula; height zeta-function de la Bretèche R., Browning T.D. , On Manin's conjecture for singular del Pezzo surfaces of degree four, I, Michigan Math. J ., in press. Zbl 1132.14019
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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. Bogomolov's conjecture; Abelian variety; torsion point; Néron-Tate height A. Abbes, Hauteurs et discrétude (d'après L. Szpiro, E. Ullmo et S. Zhang) , Astérisque 245 (1997), 141--166., Séminaire Bourbaki 1996/97, exp. 825.
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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. transcendence of elliptic modular functions in characteristic \(p\); Tate elliptic curve; theorem of Siegel and Schneider; transcendence of periods of elliptic curves; Mahler-Manin conjecture; elliptic logarithm [V1] J. F. Voloch:Transcendence of elliptic modular functions in characteristic p, J. Number Theory58 (1996) 55-59.
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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; subvarieties of \({\mathbb G}_m^n\); Bogolomov's conjecture Wolfgang M. Schmidt, Heights of points on subvarieties of \?\(^{n}\)_{\?}, Number theory (Paris, 1993 -- 1994) London Math. Soc. Lecture Note Ser., vol. 235, Cambridge Univ. Press, Cambridge, 1996, pp. 157 -- 187.
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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 on rational points; function fields; Hirzebruch surface; height zeta-function David Bourqui, Fonction zêta des hauteurs des surfaces de Hirzebruch dans le cas fonctionnel, J. Number Theory 94 (2002), no. 2, 343-358 (French, with English summary).
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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 function; distribution of integral points; arithmetic order; Faltings' theorem; rational points; Mordell's conjecture J. H. Silverman, ''Integral points on curves and surfaces'' in Number Theory (Ulm, Germany, 1987) , Lecture Notes in Math. 1380 , Springer, New York, 1989, 202--241.
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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. Beilinson conjectures; Birch-Swinnerton-Dyer conjecture; Shimura- Taniyama-Weil conjecture; Tate conjectures; Hasse-Weil conjecture; Hodge conjecture; Hodge cycles; Grothendieck conjectures; mixed motives; Grothendieck's conjectures; Fermat's last theorem; Bloch-Kato conjecture; Tamagawa numbers Hulsbergen, Conjectures in arithmetic algebraic geometry (1994)
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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 curves; Mordell-Weil rank; Lang's conjecture; rational point; variety of general 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. Heights; subvarieties of tori; Bogomolov's conjecture; small points F. Amoroso and E. Viada, Small points on subvarieties of a torus. Duke Mathematical Journal 150(3) (2009), 407-442. MR2582101
| 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; modular elliptic curve; modular deformation; Shimura-Taniyama-Weil conjecture; Selmer groups; survey article; universal deformation ring; Hecke ring G. Darmon, The Shimura-Taniyama conjecture (after Wiles), Uspekhi Mat. Nauk 50 (1995), no. 3(303), 33 -- 82 (Russian); English transl., Russian Math. Surveys 50 (1995), no. 3, 503 -- 548.
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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. Frey curve; Taniyama-Weil conjecture; survey; Fermat's Last Theorem; elliptic curves; Galois representations; \(L\)-functions; group of rational points; level reduction
| 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 last theorem; ABC-conjecture; Szpiro's conjecture; absolute value of the minimal discriminant; asymptotic Fermat conjecture; conjecture of Shimura-Taniyama-Weil; Serre's conjecture about modular representations Frey, G., Links between solutions of \(A - B = C\) and elliptic curves, (Number Theory, Ulm, 1987, Lecture Notes in Math., vol. 1380, (1989), Springer New York), 31-62
| 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. bounded height conjecture; semi abelian varieties; Weil height; anomalous subvarieties
| 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 restriction; Néron model; abelian variety; Grothendieck's duality conjecture; obstruction to extending the Poincaré bundle Néron, A.: Modèles Minimaux des Variétés Abéliennes sur les Corps Locaux et Globaux. Publications Mathématiques de l'IHÉS, vol. 21, Institut des Hautes Études Scientifiques, Paris (1964)
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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; function fields; heights; \(S\)-units; integral 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. arithmetic of curves; Diophantine problems; Faltings' theorem; Shafarevich's conjecture; Mordell's conjecture; height Grothendieck, A.: Techniques de construction et théorèmes d'existence en géométrie algébrique. IV (FGA). Les schémas de Hilbert. In: Séminaire Bourbaki, vol. 6, pages Exp. No. 221, 249-276. Soc. Math. France, Paris (1995)
| 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. height functions; projective varieties; canonical heights; Néron-Tate heights; abelian varieties; Silverman heights on K3-surfaces; heights on curves; Northcott's finiteness theorem Talamanca, V.: Height preserving linear transformations on linear spaces. (1995)
| 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 curve; Shimura-Taniyama-Weil conjecture; Szpiro's conjecture Dorian Goldfeld, Modular elliptic curves and Diophantine problems, Number theory (Banff, AB, 1988) de Gruyter, Berlin, 1990, pp. 157 -- 175.
| 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 curves; heights; height 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. Siegel's lemma; adelic geometry of numbers; lattice points; successive minima; minimal vectors; adelic fibre bundles; adelic van der Corput inequality Éric Gaudron, Géométrie des nombres adélique et lemmes de Siegel généralisés, Manuscr. Math.130 (2009), p. 159-182
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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 diophantine equations; Mordell's equation; algorithms; Hall's conjecture; large integer points; large generators; Mordell-Weil group; large Tate-Shafarevich groups; distribution of integer points Gebel, J.; Petho, A.; Zimmer, H. G., On mordell\(###\)s equation, Compos. Math., 110, 335-367, (1998)
| 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. André-Oort conjecture; Pink's conjecture; linear forms in logarithms; mixed Shimura varieties; variation of Faltings height Wüstholz, Gisbert, A note on the conjectures of André-Oort and Pink with an appendix by Lars Kühne, Bull. Inst. Math. Acad. Sin. (N.S.), 9, 4, 735-779, (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. optimal elliptic curve; strong Weil uniformization; Drinfeld modular curve; rigid-analytic uniformization; Néron model; connected component; monodromy pairing; conductor; \(j\)-invariant; inseparability degree; Szpiro's conjecture Mihran Papikian, Pesenti-Szpiro inequality for optimal elliptic curves, J. Number Theory 114 (2005), no. 2, 361 -- 393.
| 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 zeta function; rational points; equivariant compactification; Fourier analysis; Manin's conjecture A. Chambert-Loir , Y. Tschinkel , Points of bounded height on equivariant compactifications of vector groups, I . Compositio Math. 124 ( 2000 ), n^\circ 1 , 65 - 93 . MR 1797654 | Zbl 0963.11033
| 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; Beauville's ``splitting property'' conjecture; Bloch-Beilinson filtration; Chow groups; Fano variety; \(K3\) surface; motive; 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. Jacobian of the modular curve; modular elliptic curve; class number problem; infinite order point in Mordell-Weil group; heights of Heegner points; Rankin L-series; holomorphic continuations; functional equations; conjecture of Birch and Swinnerton-Dyer Gross, B. H.; Zagier, D. B., Heegner points and derivatives of \textit{L}-series, Invent. Math., 84, 225-320, (1986)
| 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; Lehmer problem; multiplicative group Amoroso, F.; David, S.: Minoration de la hauteur normalisée des hypersurfaces. Acta arith. 92, 339-366 (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. Bloch-Beilinson conjecture; special values; Hasse-Weil \(L\)-function; Deligne'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. Poincaré series for p-adic points on a variety; arithmetic theory of polynomials; Siegel-Weil formula; forms of higher degree; generalized Poisson formula; local zeta function; Bernshtein's theorem; Denef's theorem; rationality; zeta distributions; invariants for prehomogeneous vector spaces; poles
| 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. rational point; product theorem; abelian variety; abelian subvariety; Mordell's conjecture; ample symmetric invertible sheaf; Néron-Tate height pairing; Faltings' product 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. optimal curve; isogeny class; indecomposable polarization; hermitian module; Serre's obstruction; plane quartic; Siegel modular form; Hasse-Weil-Serre bound Ritzenthaler, C.: Optimal curves of genus 1, 2 and 3, Publ. math. Besançon, 99-117 (2011)
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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's lemma; successive minima; adelic vector bundle; combinatorial Nullstellensatz Gaudron, É.; Rémond, G., Lemmes de Siegel d'évitement, Acta Arith., 154, 125-136, (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. Shimura-Taniyama-Weil conjecture; elliptic curve; \(ABC\) conjecture; height conjecture; degree conjecture; Phragmén-Lindelöf theorem; \(L\)- functions; modular curves Liem Mai and M. Ram Murty, The Phragmén-Lindelöf theorem and modular elliptic curves, The Rademacher legacy to mathematics (University Park, PA, 1992) Contemp. Math., vol. 166, Amer. Math. Soc., Providence, RI, 1994, pp. 335 -- 340.
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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 curves; algebraic curves; group schemes; modular functions; \(L\)-functions; theta functions; Fermat's last theorem; conjecture of Birch and Swinnerton-Dyer; Shimura-Taniyama-Weil conjecture; Calabi-Yau varieties; string theory; cryptography; Hopf algebroids; elliptic cohomology Husemöller, D.: Elliptic Curves. Graduate Texts in Mathematics, 2nd edn. Springer, Berlin (2004)
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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 function; Mordell's conjecture; twisted Fermat curves; dual pairs of type II; symplectic form; unitary groups; irreducible dual reductive pairs; parabolic subgroups; non-ramified type I dual reductive pairs; irreducible admissible representations; Hecke algebras DOI: 10.1112/plms/s3-55.3.465
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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's last theorem; proof of the Taniyama-Weil conjecture; elliptic curves; semistable curves; Hecke algebra of a modular curve; \(p\)-adic Galois representation Wiles, Andrew, Modular elliptic curves and fermat\(###\)s last theorem, Ann. of Math. (2), 141, 3, 443-551, (1995)
| 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. survey; Thue equation; elliptic analogon of Lehmer's problem; Tate conjecture; algebraic varieties; elliptic 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. periods of an algebraic cycle; values of L-functions; higher regulators; Hodge conjecture; motives; Riemann-Roch theorem; multidimensional analog of Arakelov's construction of Néron-Tate height on curves; deformation of Chern classes; stable cohomology of current algebras Beilinson, A., Higher regulators and values of \textit{L}-functions, J. Sov. Math., 30, 2036-2070, (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. Hasse-Weil \(L\)-functions; average analytic rank of elliptic curves; height; Taniyama-Weil conjecture; ranks of the Mordell-Weil groups; Birch--Swinnerton-Dyer conjecture A. Brumer, ''The average rank of elliptic curves. I,'' Invent. Math., vol. 109, iss. 3, pp. 445-472, 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. Lehmer's problem; heights; class numbers; exponent of class group
| 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; affine automorphisms; Kawaguchi's conjecture; regular maps Lee, C., An upper bound for the height for regular affine automorphisms of \(\mathbb{A}^n\), Math. Ann., 355, 1, 1-16, (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. \(p\)-adic heights; abelian varieties with split multiplicative reduction; rigid analytic uniformization; local height pairing; theta functions on the covering torus
| 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. Baker's method; lower bound for linear forms in logarithms of algebraic numbers; relative logarithmic Weil height; Kummer descent; extrapolation technique Baker, A.; Wüstholz, G., Logarithmic forms and group varieties, J. Reine Angew. Math., 442, 19-62, (1993)
| 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. Grothendieck rings of varieties; motivic integration; heights; Poisson formula; Manin's conjecture; vanishing cycles; Euler products
| 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. rational points; del Pezzo surface; conic bundle surface; Batyrev-Manin conjecture; Thue-Siegel-Roth theorem; anticanonical height DOI: 10.4064/aa163-3-6
| 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. smooth affine surface; affine curve; finite morphism; degree of finite morphism; Euler characteristic; ramification divisor; height; log-Kodaira dimension; Vojta's conjecture; algebraically degenerate holomorphic curve Corvaja, Pietro; Zannier, Umberto, Algebraic hyperbolicity of ramified covers of \(\mathbb {G}^2_m\) (and integral points on affine subsets of \(\mathbb {P}_2\)), J. Differential Geom., 0022-040X, 93, 3, 355\textendash 377 pp., (2013)
| 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 equations; \(S\)-unit equations; decomposable form equations; discriminant form equations; elliptic curves; Mordell-Weil theorem; curves of genus greater than one; resolution of Thue-Mahler equations; sieve methods; index form equations; rational points; hyperelliptic curves; superelliptic equations; Fermat curves; Catalan's equation Smart N.\ P., The algorithmic resolution of Diophantine equations, London Math. Soc. Stud. Texts 41, Cambridge University Press, Cambridge 1998.
| 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. p-adic L-functions; p-adic height of Heegner points; Weil elliptic curve; conjecture of Birch and Swinnerton-Dyer PERRIN-RIOU (B.) . - Fonctions L p-adiques et points de Heegner , Journées arithmétiques de Besançon, Société Mathématique de France, Astérisque, n^\circ 147-148, 1987 , p. 151-171. Zbl 0636.14005
| 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. families of abelian varieties; number of geometric points; canonical heights; Weil height; local height pairings
| 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. arithmetic fundamental lemma; arithmetic Gan-Gross-Prasad conjecture; Kudla-Rapoport special divisor; relative trace formula; unitary Shimura variety; Weil representation
| 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. function fields; Weil height; Bogomolov 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. big height; finite super heigth; direct summand conjecture; improved monomial conjecture; Zariski's main theorem Koh, Jee, Finite super height of a homogeneous ideal in \({\mathbf Z}^n\)-graded extensions, J. Algebra, 109, 2, 334-351, (1987)
| 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. theta divisor; Neron-Tate height; arbitrary genus; projective varieties; Falting's theorem; algebraic curve; rational points; Szpiro's conjecture; jacobians; elliptic curves De Diego, T.: Points rationnels sur LES familles de courbes de genre au moins 2. J. number theory 67, 85-114 (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. nonisolated hypersurface singularities; Milnor fibration; morsification; equisingularity; Zariski's multiplicity conjecture; topological triviality; Floer homology; lattice homology; low dimensional topology; plumbing 3-manifolds; simultaneous resolutions; \(\mu\)-constant families; isolated surface singularities; topological triviality; Lipschitz equisingularity; motivic integration; arc spaces; vanishing cycles; monodromy; vanishing folds; cobordism theorem; computer algebra system ``Singular''
| 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 varieties over finite fields; \(L\)-functions; zeta functions; \(p\)-adic analysis; Dwork's conjecture Wan, D., Higher rank case of dwork\(###\)s conjecture, J. Amer. Math. Soc., 13, 807-852, (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. conjecture of Harder; congruences between Siegel modular forms of genus 1 and 2; Eisenstein cohomology Gerard van der Geer, ``Siegel Modular Forms'', , 2007
| 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. analytic superspaces; GAGA; Chow's lemma; families of compact super Riemann surfaces Rabin, J. M.; Topiwala, P.: Super Riemann surfaces are algebraic curves. (1988)
| 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. decidability; Hilbert's Tenth Problem; uncomputably large integral points on algebraic curves; diophantine prefix; polynomials; height bounds; geometry of complex surfaces and 3-folds J.M. Rojas, Uncomputably large integral points on algebraic plane curves?, Theoret. Comput. Sci., 235 (this Vol.) (2000) 145--162.
| 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 series; \(L\)-functions of symmetric powers of elliptic curves; Beilinson's conjecture; motivic cohomology groups; Bloch-Beilinson regulator; de Rham cohomology Mestre, J. -F.; Schappacher, N.: Séries de Kronecker et fonctions L des puissances symétriques de courbes elliptiques sur Q. Progr. math. 89, 209-245 (1991)
| 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. Waldschmidt constant; Demailly's conjecture; Chudnovsky's conjecture; Nagata-Iarrobino 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. hyperbolic fibre space; higher dimensional analogue of Mordell's conjecture for curves; hyperbolic manifolds; algebraic families of hyperbolic varieties; Mordell's conjecture over function fields Noguchi, J.Hyperbolic fiber spaces and Mordell's conjecture over function fields, Publ. Research Institute Math. Sciences Kyoto University21, No. 1 (1985), 27--46.
| 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. Bogomolov property; elliptic curve; Weil height; Néron-Tate height
| 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; curves over finite fields; Vojta's conjecture Corvaja, P.; Zannier, U., Greatest common divisors of \(u - 1\), \(v - 1\) in positive characteristic and rational points on curves over finite fields, J. Eur. Math. Soc., 15, 1927-1942, (2013)
| 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. Hilbert's tenth problem; elliptic curve; Mazur's conjecture; diophantine definition B. Poonen, ''Hilbert's Tenth Problem and Mazur's Conjecture for Large Subrings of \(\mathbb{Q}\),'' J. Am. Math. Soc. 16(4), 981--990 (2003).
| 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. Viehweg's hyperbolicity conjecture; log general type; log cotangent bundle; foliation; movable curve class; slope semi-stability
| 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. finite generation of invariant algebra; Hilbert's fourteenth problem; Popov-Pommerening conjecture Tan, L., \textit{some recent developments in the Popov-pommerening conjecture}, Group actions and invariant theory, 207-220, (1989), American Mathematical Society, Providence, RI
| 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. theta series; slopes; Siegel modular form; Fourier-Jacobi expansion; Schottky's polynomial; moduli space Salvati Manni, R.: Modular forms of the fourth degree. (Remark on a paper of Harris and Morrison). Proc. Conf., Trento/Italy 1990, Lect. Notes Math., vol. 1515, pp. 106--111 (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. real algebraic geometry; real algebraic varieties; complexification; Smith's theory; Galois-Maximal varieties; algebraic cycles; real algebraic models; algebraic curves; algebraic surfaces; topology of algebraic varieties; regular maps; rational maps; singularities; algebraic approximation; Comessatti theorem; Rokhlin theorem; Nash conjecture; Hilbert's XVI problem; Cremona group; real fake planes
| 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. Zariski's multiplicity conjecture; topological V-equivalent; topologically equisingular; Le number; aligned singularities Eyral C., IMPAN Lecture Notes 3, in: Topics in Equisingularity Theory (2016)
| 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; Hadamard's theorem; global inversion theorem Balreira, E., Foliations and global inversion, Comment. Math. Helv., 85, 73-93, (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. affine congruences; rational points; Manin's conjecture; cubic surfaces; universal torsors Boudec, P, Affine congruences and rational points on a certain cubic surface, Algebra Number Theory, 8, 1259-1296, (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. dimension of obstruction space for deformations; cyclic quotient singularity; Wahl's conjecture Christophersen, J. , Monomial curves and obstructions on cyclic quotient singularities, in 'Singularities, representations of algebras and vector bundles, Lambrecht 1985 ,' Lecture Notes in Mathematics 1273, Springer Verlag, Berlin-Heidelberg- New York.
| 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. Galois lattice structure of the Mordell-Weil group; height pairing; L-function; Hasse zeta function; computer calculations Shioda, T.: The Galois Representations of TypeE 8 Arising from Certain Mordell-Weil Groups, Proc. Japan Acad.65A, 195--197 (1989)
| 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. multiplicative dependence; absolute logarithmic height; height of points on curves Cohen, Paula B.; Zannier, Umberto, Multiplicative dependence and bounded height, an example.Algebraic number theory and Diophantine analysis, Graz, 1998, 93-101, (2000), de Gruyter, Berlin
| 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. modular curve; jacobian; abelian variety; \({\mathbb{Q}}\)-simple factors; torsion subgroups of the Mordell-Weil groups; conjecture of Birch and Swinnerton-Dyer
| 0 |
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