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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. Lang conjecture; heights; polarized Abelian variety Moriwaki, A.: A generalization of conjectures of bogomolov and lang over finitely generated fields. Duke math J 107, No. 1, 85-102 (2001)
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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. Faltings' proof of Lang's conjecture; rational points on subvarieties of Abelian varieties; semi-Abelian 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. Efimov's theorem; Euclidean 3-space; immersed surface; Riemannian metric; Gauss curvature; Milnor's conjecture; diffeomorphism; Jacobian conjecture; global asymptotic stability of dynamical system
| 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. resolutions; Green's conjecture Vélu, J.: Courbes elliptique munies d'un sous-group \(\mathbb{Z}/n\mathbb{Z}\times \mu _n\), Bull. Soc. Math. France, Mémoire \textbf{57} (1978)
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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. Berthelot's conjecture; arithmetic \(\mathcal{D}\)-modules; overconvergent \(F\)-isocrystals; \(p\)-adic cohomology Lazda, Christopher, Incarnations of Berthelot's conjecture, J. Number Theory, 166, 137-157, (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. linear Diophantine equations; quadratic Diophantine equations; multiplicative Diophantine equations; rational points; curves of genus \(0, 1, (>1)\); Runge theorem; Thue-Siegel theorems; p-adic method; representability of integers by binary quadratic forms Th. Skolem, Diophantische Gleichungen, Chelsea, 1950.
| 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 lattice; supersingular; rational points; rational elliptic surface; height pairing; Mordell-Weil groups J. Wolfard, \textit{ABC for polynomials, dessins d}'\textit{enfants, and uniformization} -- \textit{a survey}, in \textit{Proceedings der ELAZ-Konferenz} 2004, W. Schwarz and J. Steuding eds., Steiner Verlag, Stuttgart, Germany, (2006), pg. 313.
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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. polynomials; Lojasiewicz's inequality; transcendence measures; approximation measures; logarithmic size; common zeros Francesco Amoroso, Values of polynomials with integer coefficients and distance to their common zeros, Acta Arith. 68 (1994), no. 2, 101 -- 112.
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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. Mahler measure; Bloch conjecture; Beilinson conjectures; modular form; regulator; K-theory; elliptic curve; mirror symmetry; L-function F. Rodriguez Villegas, \textit{Modular Mahler measures, I}, in \textit{Topics in number theory}, Kluwer Acad. Publ., Dordrecht, The Netherlands (1999), p. 17.
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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. reflexive differentials; Viehweg's hyperbolicity 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. intersection ring; Grothendieck group; \(\gamma\)-filtration; rational equivalence; Chow's moving lemma; algebraic cycles; relative Chow group Consani, C., A moving-lemma for a singular variety and applications to the Grothendieck group \(K\)\_{}\{0\}(\(X\)), Santa Margherita Ligure, 1989, Providence
| 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. lattices and their invariants; associated tori; elliptic functions; modular forms of one variable; periodic meromorphic functions; field of elliptic functions; Weierstrass \(\wp\)-function; elliptic curves; product representations; complex multiplication; Jacobi's theta series; Jacobi forms; modular functions; Siegel modular group; discontinuous subgroups; weight formula; Dedekind's eta-function; cusp forms; algebra of Hecke operators; Petersson inner product; Eisenstein series; Dirichlet series; functional equation; Hecke operators; harmonic polynomials; quadratic forms; Epstein zeta-function; Kronecker's limit formula; Rankin convolution M. Koecher and A. Krieg, \textit{Elliptische Funktionen und Modulformen}, Springer, Berlin, Heidelberg, 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. constructible sheaf; cohomology of curves; Poincaré duality; proof of Weil conjecture; base change; Lefschetz trace formula; cycle map; rationality of L-series Milne, J. S.: Étale Cohomology. Princeton Univ. Press (1980)
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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. Diophantine equations; arithmetic algebraic geometry; heights; Mordell-Weil theorem; integral points lang S.~Lang, \emph Fundamentals in Diophantine Geometry, Springer, New York, 1983.
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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. truncated cube; nestohedron; associahedron; Gal's conjecture; Dynkin diagram; nested polytope Buchstaber, V M; Volodin, V D, Combinatorial 2-truncated cubes and applications, No. 299, 161-186, (2012), 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. formal groups; cobordism; projective complex space; Milnor manifold; Chern characteristic classes; natural multiplicative transformation; Chern-Novikov character; logarithm; exponent; K-theory; generating function; Hirzebruch's genus; Toda's genus; virtual arithmetical genus; Euler formal group; elliptic function V. M. Bukhshtaber and A. N. Kholodov, ''Formal Groups, Functional Equations, and Generalized Cohomology Theories,'' Mat. Sb. 181(1), 75--94 (1990) [Math. USSR, Sb. 69, 77--97 (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. elliptic \(K3\) surface; torsion section; conjectures of Shioda and Artin; Artin invariant; height of a formal Brauer group; Mordell-Weil group; supersingular \(K3\) surface Ito, Hiroyuki; Liedtke, Christian, Elliptic K3 surfaces with \(p^n\)-torsion sections, J. Algebraic Geom., 1056-3911, 22, 1, 105-139, (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. Murre's conjecture; motivic decomposition; Chow group; curve; abelian variety; elliptic modular threefold; product varieties Xu, K; Xu, Z, Remarks on murre's conjecture on Chow groups, J. K-Theo., 12, 3-14, (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. exceptional collection; exceptional sequence, tilting sheaf, King's conjecture; full strong exceptional collection Michalek M.: Family of counterexamples to King's conjecture. Comptes Rendus Math. 349(1-2), 67--69 (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. family of curves; large monodromy; finite ground field; numerator of the zeta function; Katz's conjecture Chavdarov, N., \textit{the generic irreducibility of the numerator of the zeta function in a family of curves with large monodromy}, Duke Math. J., 87, 151-180, (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. Nevanlinna theory; holomorphic curves; algebraic variety; Bloch's conjecture Kobayashi, R., Holomorphic curves into algebraic subvarieties of an abelian variety.Internat. J. Math., 2 (1991), 711--724.
| 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 ground fields; Hodge-Tate modules; Tate conjecture; \(\ell\)-adic representation; elliptic curves; Taniyama-Weil conjecture Serre, Jean-Pierre, Abelian \(l\)-adic representations and elliptic curves, Research Notes in Mathematics 7, 199 pp., (1998), A K Peters, Ltd., Wellesley, MA
| 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. semistable vector bundles; moduli; Beauville's conjecture; theta map; complex projective curve Brivio, S.; Verra, A., \textit{Plücker forms and the theta map}, Amer. J. Math., 134, 1247-1273, (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. preperiodic points; dynamical Manin-Mumford; Zhang's height; Julia sets; capacity theory Mimar, A., \textit{on the preperiodic points of an endomorphism of 1 {\(\times\)}1 which Lie on a curve}, Trans. Amer. Math. Soc., 365, 161-193, (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. Fano threefolds; geometric Manin's conjecture; Batyrev's conjecture; moduli spaces of rational 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. Kronecker elimination theory; components of an algebraic set; Cayley- Severi form; Barsotti-Siegel-Weil forms
| 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. étale chain complexes; reductive algebraic group; Deligne-Lusztig variety; splendid equivalence; proof of Broué's conjecture; étale sheaves; pure derived categories Raphaël Rouquier, Complexes de chaînes étales et courbes de Deligne-Lusztig, J. Algebra 257 (2002), no. 2, 482 -- 508 (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. Poisson Noether's problem; Poisson rationality; Calogero-Moser spaces; Cherednik algebras; Gelfand-Kirillov 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. \(ABC\) conjecture; heights; elliptic curve Mochizuki, Sh.: Arithmetic elliptic curves in general position. Math. J. Okayama Univ. \textbf{52}, 1-28 (2010) (with comments at http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html)
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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. mixed motives; finite fields; Weil zeta-function; Tannakian categories; Tate conjecture; homological algebra Milne, James S.; Ramachandran, Niranjan, Integral motives and special values of zeta functions, Journal of the American Mathematical Society, 17, 499-555, (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. order of Tate-Shafarevich group; Birch Swinnerton-Dyer conjecture; Weil curve J. Buhler, B. Gross and D. Zagier: On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank 3. Math. Comp., 44, 473-481 (1985). JSTOR:
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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. hypersurface; Lang-Weil bound; Bertini's theorem; random sampling
| 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. section; del Pezzo fibration; Fujita invariant; geometric 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. quantization; Frobenius manifolds; Gromov-Witten potential; moduli of curves; r-spin structures; Witten's conjecture C. Faber, S. Shadrin, and D. Zvonkine, Tautological relations and the \(r\)-spin Witten conjecture, Ann. Sci. Éc. Norm. Supér. (4) 43 (2010), 621--658.
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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. discriminant conjecture for elliptic curves; function field; Frey curves; Weil curves Szpiro, L., Discriminant et conducteur des courbes elliptiques, Séminaire sur les Pinceaux de Courbes Elliptiques, Paris, 1988, Astérisque, 183, 7-18, (1990)
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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. \(\mathbb{A}^1\)-connected components; \(\mathbb{A}^1\)-chain connected components; Morel'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. real geometry; semi-algebraic sets; Thom's 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. fundamental group of the complement of a hypersurface fundamental group of a knot; Zariski's conjecture; commutativity of the fundamental group Kulikov Vik.S., A remark on classical Pluecker's formulae, preprint available at http://arxiv.org/abs/1101.5042
| 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 Néron-Tate height; p-adic Birch-Swinnerton-Dyer conjecture; Tate-Shafarevich group; elliptic curve; p-adic L-function
| 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; Mordell-Lang problem; 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. elliptic scheme; elliptic surface; torsion points; Betti map; o-minimality; canonical height; Roth'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. Mukai's conjecture; syzygies
| 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 curves; Manin's conjecture; Fujita invariant
| 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. Bloch's conjecture; Chow group; zero cycles
| 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. adjoint system; log canonical singularities; Kawamata log terminal singularities; Cartier divisor; Fujita's freeness conjecture Yujiro Kawamata, ``On Fujita's freeness conjecture for \(3\)-folds and \(4\)-folds'', Math. Ann.308 (1997) no. 3, p. 491-505
| 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; rational points; anomalous intersections; Mordell-Lang 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. Brody hyperbolicity; minimal models; moduli of polarized varieties; varieties of general type; Green-Griffiths-Lang's conjecture; Hodge modules
| 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; Wright'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. elliptic curves; canonical height; non-archimedean heights; algorithm; factorization J. H. Silverman, Computing canonical heights with little (or no) factorization.Math. Comp. 66 (1997), 787--805.
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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; normalised height; Lehmer problem
| 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 curves; ranks of the Mordell-Weil groups; ranks of the groups of rational points; Shimura-Taniyama-Weil conjecture; Birch-Swinnerton-Dyer conjecture S. Fermigier, Étude expérimentale du rang de familles de courbes elliptiques sur \(\mathbb{Q}\)
\[
\mathbb{Q}
\]
. Exp. Math. 5 (2), 119--130 (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. Frobenius splitting; spherical varieties; Wahl'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. Hurwitz schemes; branch covers; Malle's conjecture S. Türkelli, Connected components of Hurwitz schemes and Malle's conjecture, J. Number Theory 155 (2015), 163--201.
| 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. Igusa zeta functions; rationality in positive characteristic; Igusa'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. mirror symmetry conjecture; Schoen's Calabi-Yau 3-fold; complete intersection; toric variety; Yukawa couplings; theta function; eta function; Gromov-Witten invariants Hosono, S., Saito, M-H., Stienstra, J.: On the mirror symmetry conjecture for Schoen's Calabi-Yau 3-folds. In: Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), World Sci. Publishing, River Edge, NJ, 1998, pp. 194--235
| 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. Xiao's conjecture; algebraic surface; birational geometry; canonical fibration; family of 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. Thom's first isotopy lemma; Nash triviality Coste, M., Shiota, M.: Thom's first isotopy lemma: a semialgebraic version, with uniform bound. In: ''Real Analytic and Algebraic Geometry (Trento, 1992)'', pp. 83-101. de Gruyter, Berlin (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. C-M field; abelian variety; center of critical strip of \(L\)-functions; special values of \(L\)-functions; Deligne's general conjecture Gross, B. H., \textit{L}-functions at the central critical point, Motives, Seattle, WA, 1991, 527-535, (1994), 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. Birch Swinnerton-Dyer conjecture; elliptic curves; height of the Heegner points; derivative of the L-series; class number 3 problem D. Zagier, ''\(L\)-series of elliptic curves, the Birch-Swinnerton-Dyer conjecture, and the class number problem of Gauss,'' Notices Amer. Math. Soc., vol. 31, iss. 7, pp. 739-743, 1984.
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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; abelian variety; Bogomolov's conjecture; Arakelov geometry Szpiro, L.; Ullmo, E.; Zhang, S., Équirépartition des petits points, Invent. Math., 127, 337-347, (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. Fujita's conjecture; adjoint bundles; global generation; very ampleness
| 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 lemma; constructive algebra; computational algebra; program extraction; proof mining
| 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. Dirichlet motives; modular curves; motivic cohomology; Hodge structures; Galois modules; Tate motives; Beilinson's conjecture for Dirichlet \(L\)-functions Huber, A.; Kings, G., \textit{Dirichlet motives via modular curves}, Ann. Sci. Éc. Norm. Supér (4), 32, 313-345, (1999)
| 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. Gersten's conjecture; characteristic \(p\); finiteness of \(p\)-torsion of zero-cycles; purity theorems for logarithmic Hodge-Witt sheaves; Cousin complex N. Suwa, ''A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves,'' \(K\)-Theory, vol. 9, iss. 3, pp. 245-271, 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. Kempf's vanishing theorem; cohomology of line bundles; flag varieties; Borel-Weil 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. \(K_n\)-regularity; cdh-descent; Hochschild homology; cyclic homology; smoothness; Vorst's conjecture Cortiñas, G.; Haesemeyer, C.; Weibel, C., \(K\)-regularity, \(cdh\)-fibrant Hochschild homology, and a conjecture of Vorst, J. Amer. Math. Soc., 21, 2, 547-561, (2008)
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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. Chabauty's theorem; number of rational points; Mordell-Weil group; hyperelliptic curve Flynn, E.V.; A flexible method for applying Chabauty's theorem; Compos. Math.: 1997; Volume 105 ,79-94.
| 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. del Pezzo surface; Manin's conjecture; nef cone; root system U. Derenthal, M. Joyce, and Z. Teitler, ''The nef cone volume of generalized del Pezzo surfaces,'' Algebra Number Theory, 2, No. 2, 157--182 (2008).
| 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. generic morphism; branch curve; discriminant curve; Chisini's conjecture; surface of general type; braid monodromy; cuspidal algebraic curves Kulikov S.\ V. and Teicher M., Braid monodromy factorizations and diffeomorphism types, Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000), no. 2, 89-120.
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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. monoids; affine semigroups; base point free; Mori dream spaces; Fujita's freeness 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. height; Weil height; rational map Ghioca, Dragos; Mavraki, Niki Myrto, Variation of the canonical height in a family of rational maps, New York J. Math., 19, 873-907, (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. Siegel modular varieties; Runge's method; good 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. semilocal rings; weak local-global principle; prime ideal theorem; Pfister's local-global principle; real spectrum; real algebraic geometry; semialgebraic sets; constructible sets; Separation theorem; maximal orderings; signatures; Witt rings; Knebusch conjecture; bilinear forms over rings Murray A. Marshall, Bilinear forms and orderings on commutative rings, Queen's Papers in Pure and Applied Mathematics, vol. 71, Queen's University, Kingston, ON, 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. Grothendieck's conjecture; hyperbolic algebraic curves; étale fundamental groups; arithmetic fundamental groups; anabelian conjectures; \(p\)-adic Grothendieck conjecture; birational Grothendieck conjecture Nakamura, H.; Tamagawa, A.; Mochizuki, S.: The Grothendieck conjecture on the fundamental groups of algebraic curves. Sugaku expositions 14, 31-53 (2001)
| 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. Xiao's conjecture; relative irregularity; plane curves; Jacobian ideals
| 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. bidisk; Christofffel-Darboux; sums of squares; Fejér-Riesz; orthogonal polynomials; distinguished varieties; Pick interpolation; Ando's inequality; Bernstein-Szegő measures; torus; stable polynomials G. Knese, ''Polynomials with no zeros on the bidisk,'' Anal. PDE, vol. 3, iss. 2, pp. 109-149, 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. Manin's conjecture; Châtelet surfaces; reducible; weak approximation Bretèche, R.; Browning, T. D.; Peyre, E., On Manin's conjecture for a family of Châtelet surfaces, Ann. of Math., 175, 297-343, (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. curves of low genus; quadratic sequences; Mohanty's conjecture; function field arithmetic
| 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. Picard group; non-commutative crepant resolution; Gabber's conjecture; punctured spectrum; Hochster's theta function DOI: 10.1112/S0010437X11005513
| 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. lemma of tangents; segre's generalization of the theorem of Menelaus; Hermitian curves; semiovals; circle geometries; linear MDS codes; linear maximum distance separable codes
| 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; G-functions; algebraic functions; Hilbert's irreducibility theorem; height on abelian varieties Dèbes, P.: G-fonctions et théorème d'irréductibilité de Hilbert. Acta arith. 47 (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. Nagata's conjecture; linear systems; plane curves C. Ciliberto, B. Harbourne, R. Miranda, J. Ro'e, \textit{Variations of Nagata's conjecture}, in: A Celebration of Algebraic Geometry, Clay Math. Proc. 18, Amer. Math. Soc., Providence, RI, 2013, 185--203. [13] C. Ciliberto, R. Miranda, \textit{Degenerations of planar linear systems}, J. Reine Angew. Math. 501 (1998), 191--220.
| 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. Thom's lemma; coding of real algebraic numbers; cylindric algebraic decomposition of a semialgebraic set 8. M. COSTE et M.-F. ROY, Thom's Lemma, the Coding of Real Algebraic Numbers and the Computation of the Topology of Semi-AIgebraic Sets, J. Symbolic Computations, 1988, 5, p. 121-129. Zbl0689.14006 MR949115
| 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. Miller's algorithm; pairing computation; Edwards curves; Tate/Weil 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. morphisms; Chow's lemma; Grothendieck existence theorem; coherent sheaves Martin Olsson, ``On proper coverings of Artin stacks'', Adv. Math.198 (2005) no. 1, p. 93-106
| 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 points; Diophantine approximation; Schmidt's subspace theorem; Vojta's main 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. flag variety; positive characteristic; heights; zeta function; Manin conjecture Peyre, E, Points de hauteur bornée sur LES variétés de drapeaux en caractéristique finie, Acta Arith., 152, 185-216, (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. logarithmic Kodaira dimension; Nakayama's numerical Kodaira dimension; affine varieties; Iitaka conjecture, minimal model program, abundance 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. Serre's conjecture; Galois representations; crystalline cohomology M. M. Schein, Weights in Serre's conjecture for \(\mathrm{GL}_{n}\) via the Bernstein-Gelfand-Gelfand complex , J. Number Theory 128 (2008), 2808-2822.
| 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 formal fibers; formal fibers of local rings; Noether's normalization 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. Mordell-Weil group; 11-torsion; 2-descent; elliptic curve; rational point of order 11; Birch Swinnerton-Dyer conjecture Ian Connell, Elliptic curve handbook, preprint, available at http://www.ucm.es/ BUCM/mat/doc8354.pdf.
| 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 curves; canonical heights; Archimedean local heights; height constant; rational points; number fields
| 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. first-order deformation; isotrivial fibration; adjoint image; supporting divisor; families of curves; unitary bundle; Xiao'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. Abhyankar's conjecture; covering of affine line; Sylow \(p\)-group; Galois group of covering
| 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. curves of higher genus; JFM 56.0180.05; finiteness of integral points on curves; Gelfond-Baker method; effective version of Siegel's theorem; Galois coverings
| 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; del Pezzo surface; degree 4; singularity; asymptotic formula Boudec, P, Manin's conjecture for two quartic del Pezzo surfaces with \(3A_1\) and \(A_1+A_2\) singularity types, Acta Arith., 151, 109-163, (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. tachyon scattering amplitudes; divisiors with complex coefficients; moduli space of complex algebraic curves of genus \(g\) with \(n\) given points; Belavin-Knizhnik theorem; bosonic string theory; Polyakov volume form; Weil-Deligne pairings; Arakelov measures; Quillen metrics
| 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. Koszul cohomology; Koszul cycles; Green's conjecture; Gonanity conjecture; Strong maximal rank conjecture Aprodu, M.; Farkas, G., Koszul cohomology and applications to moduli, Clay math. proc., 14, 25-50, (2011)
| 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. log Hodge de Rham spectral sequences in finite characteristic; log Kodaira vanishing theorem in finite characteristic; log weak Lefschetz conjecture for log crystalline cohomologies; quasi-F-split height; log deformation theory with relative Frobenius; lifts of log smooth integral schemes over \(\mathcal{W}_2\)
| 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. Ruan's conjecture; singular symplectic flops; (r,b)-orbiconifold singularity; Ruan cohomology; virtual localization Chen, B.; Li, A. -M.; Li, X.; Zhao, G., Ruan's conjecture on singular symplectic flops of mixed type, Sci. China Math., 57, 6, 1121-1148, (2014)
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