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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; del Pezzo surface; Peyre constant; volume; polytope; calculation Derenthal, U.; Elsenhans, A.; Jahnel, J., On the factor alpha in Peyre's constant, Math. Comput., 83, 965-977, (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. log terminal; Kodaira vanishing theorem; Fujita's freeness conjecture Kawamata Y.: On effective non vanishing and base-point-freeness. Asian J. Math. 4, 173--181 (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. Diophantine equations; Bogomolov-Miyaoka inequality; arithmetic surfaces; small point conjecture; effective Mordell conjecture; Szpiro conjecture; branched coverings of curves; asymptotic Fermat theorem; abc-conjecture; height; effectivity Moret-Bailly, L., Hauteurs et classes de Chern sur LES surfaces arithmétiques, Astérisque, 183, 37-58, (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. curves of genus two; Jacobians; canonical height; infinite descent; Mordell-Weil group; algorithm E.V. Flynn and N.P. Smart, Canonical heights on the Jacobians of curves of genus 2 and the infinite descent, Acta Arith., 79 (1997), 333-352. MR 98f:11066
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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. Prym variety; polarized abelian variety; Novikov's conjecture; Veselov-Novikov equation
| 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; Mordell-Weil rank; Néron-Severi group; basis for the group of rational points; elliptic surface; computer calculation; height functions Kuwata, M., The canonical height and elliptic surfaces, J. Number Theory, 36, 2, 201-211, (1990), MR 1072465
| 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. Parshin's conjecture; higher Chow group; weight homology Geisser, T.: Parshin's conjecture revisited. EMS ser. Congr. rep., 413-425 (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. projective manifolds; ample line bundles; Fujita's conjecture; global generation
| 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. 1-motives; triangulated category; Deligne's conjecture; Roitman's theorem Barbieri-Viale, L.; Kahn, B., On the derived category of 1-motives, Astérisque, 381, (2016), xi+254 pp
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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. semi-stable curves; fundamental group; Abhyankar's conjecture; Galois cover Saı\ddot{}di, M.: Raynaud's proof of abhyankar's conjecture for the affine line. Progr. math. 187, 249-265 (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. schemes and morphisms; compactification; birational morphisms; embeddings; blow-up; Chow's lemma; Nagata compactification; valuations Conrad, B., Deligne\(###\)s notes on Nagata compactification, J. Ramanujan Math. Soc., 22, 205-257, (2007)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. local Langlands conjecture; automorphic form; Shimura variety; unitary group; formal group; GL(n); Weil-Deligne group; survey Carayol, H., Preuve de la conjecture de Langlands locale pour \(\text{GL} _{n}\): travaux de harris-Taylor et henniart, No. 266, 191-243, (2000)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Vojta's main conjecture; K-stability; Fano varieties; Diophantine approximation; Newton-Okounkov bodies
| 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. secant variety; variety of reducible hypersurfaces; variety of reducible forms; intersection theory; weak Lefschetz Property; Froeberg'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. Viehweg's conjecture; maximal variation; Hodge modules; base space of families Popa, M.; Schnell, C., Viehweg's hyperbolicity conjecture for families with maximal variation, Invent. Math., 208, 3, 677-713, (2017)
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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. Kurdyka's conjecture; arc-analytic function Adamus, J; Seyedinejad, H, A proof of kurdyka's conjecture on arc-analytic functions, Math. Ann., 369, 387-395, (2017)
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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. symplectic resolution; symplectic linear quotient singularities; classification; smooth symplectic variety; Verbitsky's result
| 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; Weil conjectures; algebraic correspondences; standard conjecture of Lefschetz type doi:10.1007/s002220050140
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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. pluricanonical bundles; Fujita's conjecture; weak positivity; effective results; Seshadri constants
| 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. moduli space of curves; Faber's conjecture; tautological ring; intersection numbers; double ramification cycles Buryak, A., Shadrin, S.: A new proof of Faber's intersection number conjecture (2009). arXiv:0912.5115 [math.AG]
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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. conductor 11; parametrization of elliptic curves by modular functions; isogeny class; diophantine equation; Taniyama-Weil conjecture Agrawal, M. K.; Coates, J. H.; Hunt, D. C.; van der Poorten, A. J., Elliptic curves of conductor \(11\), Math. Comp., 35, 151, 991-1002, (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. superelliptic curve; Kummer surface; twist; Mazur'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. Iitaka's conjecture; Kodaira dimension; positive characteristic; fibration
| 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. Tate module; \(\ell \)-adic representations; Galois groups; Weil-Riemann conjecture; \(\ell \)-adic Lie algebras; dimension of Abelian variety
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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. toric varieties; Shokurov's conjecture; singularities of pairs
| 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. hard Lefschetz theorem; Grothendieck's standard conjectures; height pairings; higher Picard varieties; abelian variety; Hodge index theorem Klaus Künnemann, Higher Picard varieties and the height pairing, Amer. J. Math. 118 (1996), no. 4, 781 -- 797.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Mordell's conjecture; Faltings 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. Bogomolov's proof; Szpiro conjecture; hyperbolic geometry; symplectic geometry; upper half-plane; theta function; Gaussian distribution; inter-universal Teichmüller theory; multiradial representation; indeterminacies
| 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. Artin approximation; Néron desingularization; Bass-Quillen conjecture; Quillen's question; smooth morphisms; regular morphisms; smoothing ring morphisms Popescu, D., Artin approximation property and the general neron desingularization, \textit{Revue Roum. Math. Pures Appl.}, 62, 171-189, (2017)
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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 over number fields; Mordell-Weil rank; L-series; generalized Birch-Swinnerton-Dyer conjecture; root number Lawrence Howe, Twisted Hasse-Weil \(L\)-functions and the rank of Mordell-Weil groups, Canad. J. Math. 49 (1997), no. 4, 749-771.
| 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. klt singularity; singular Ricci-flat metric; tangent sheaf; Campana's Abelianity Conjecture; holonomy representation; Beauville-Bogomolov Decomposition Theorem; étale cover
| 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; moduli height Shaska, T.; Beshaj, L., Heights on algebraic curves.Advances on superelliptic curves and their applications, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur. 41, 137-175, (2015), IOS, Amsterdam
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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. Green's conjecture; Koszul module; canonical curve; rational normal 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. height; theorem of Mordell-Weil; v-adic metrics on a very ample line bundle; logarithmic singularities Silverman, J. H.: Theory of height functions. ''Arithmetic geometry'' (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. quartic hypersurface; Manin's conjecture; rational point; asymptotic 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. canonical Syzygy conjecture; ribbons; Green's conjecture; Koszul cohomology
| 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; nonsingular quartic del Pezzo surface; order of magnitude F.-S. Leung, Manin's conjecture on a nonsingular quartic del Pezzo surface , Acta Arith. 136 (2009), 177-199.
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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. homogeneous weight enumerator of a linear code; Duursma's zeta polynomial and Duursma's reduced polynomial of a linear code; Riemann hypothesis analogue for linear codes; formally self-dual linear codes; Hasse-Weil polynomial and Duursma's reduced polynomial of a function field of one variable Kasparian, A.; Marinov, I., Duursma's reduced polynomial, (8 May 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. finite covers of projective plane; Chisini'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. Bibliography; L-functions; regulators; algebraic cycles; Deligne-Beilinson cohomology; Yoneda extensions; mixed motives; Pell's equation; Dedekind's class number; Taylor series; Hodge conjecture; Tate's conjecture; polylogarithms; variations of mixed Hodge structures; generalized Hodge group; Birch and Swinnerton-Dyer conjectures; arithmetic varieties D. Ramakrishnan, Regulators, algebraic cycles, and values of \(L\)-functions , Algebraic \(K\)-theory and algebraic number theory (Honolulu, HI, 1987), Contemp. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1989, pp. 183-310.
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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. varieties over finite fields; étale cohomology; fundamental groups; Weil representation; Weil conjecture; deformations Pridham, J., \textit{weight decompositions on étale fundamental groups}, Amer. J. Math., 131, 869-891, (2009)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. tame generators problem; Rusek's conjecture; Keller maps; nilpotent Jacobian matrices
| 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. representation theory; reductive algebraic groups; simple G-modules; highest weights; character formula; Weyl's formula; affine group schemes; injective modules; injective resolutions; derived functors; Hochschild cohomology groups; hyperalgebra; split reductive group schemes; Steinberg's tensor product theorem; irreducible representations; Kempf's vanishing theorem; Borel-Bott-Weil theorem; characters; linkage principle; dominant weights; filtrations; Steinberg modules; cohomology ring; ring of regular functions; Schubert schemes; line bundles [6] Jantzen J.\ C., Representations of Algebraic Groups, Academic Press, Orlando, 1987
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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. Grothendieck group; cyclic Adams operations; Serre's vanishing conjecture Brown, Michael K.; Miller, Claudia; Thompson, Peder; Walker, Mark E., Cyclic {A}dams operations, Journal of Pure and Applied Algebra, 221, 1589-1613, (2017)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Galois representations; Serre's conjecture; degree 2 representations
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. numerical semigroups; symmetric numerical semigroups; Apéry set; Frobenius number; minimal presentation; monomial curves; Gröbner basis; syzygies; Betti numbers; derivation module; complete intersection; Francia's conjecture; blowup algebras; set theoretic complete intersection
| 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. colorful Carathéodory's theorem; max-plus convexity; Sierkma's conjecture; tropical geometry; Tverberg's theorem Gaubert, Stéphane; Meunier, Frédéric, Carathéodory, Helly and the others in the max-plus world, Discrete Comput. Geom., 43, 3, 648-662, (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. stratifications; Zariski equisingularity; Whitney's fibering conjecture; arc-analytic mappings Parusiński, A.; Paunescu, L., Arcwise analytic stratification, Whitney fibering conjecture and Zariski equisingularity, Adv. Math., 309, 254-305, (2017)
| 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 equation; elliptic curves; Mordell Weil group; Selmer group; Birch and Swinnerton-Dyer conjecture; parity 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. narrow Mordell-Weil lattice; group of rational points on an elliptic curve; Weyl groups as Galois groups; sphere packing; algebraic equations; inverse Galois problem; Kodaira-Néron model; height pairing; Néron- Severi group; rational elliptic surface
| 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. Dwork's conjecture; \(p\)-adic meromorphic continuation; unit root zeta function; algebraic varieties; finite field; unit root \(F\)-crystal; higher dimensional Kloosterman sums Wan D.: Dwork's conjecture on unit root zeta functions. Ann. Math. 150, 867--927 (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. Mordell-Weil group; Picard variety; function field; Tate conjecture; L-function Hindry, M., Pacheco, A.: Sur le rang des Jacobiennes sur un corps de fonctions. Bull. Soc. Math. Fr. 133, 275--295 (2005)
| 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; \(m\)-fold point; floor diagrams; tropical geometry
| 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. Deninger's conjecture; special values of \(L\)-functions; modular elliptic curve; Eisenstein-Kronecker series; regulator map Goncharov, A. B., Deninger's conjecture of \(L\)-functions of elliptic curves at \(s = 3\), J. Math. Sci., 81, 3, 2631-2656, (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. Hilbert modular variety; signature defect; explicit formula; Hirzebruch's conjecture [Sc2] Sczech, R.: Cusps on Hilbert modular varieties and values of L-functions. In: Hashimoto, V. Namikawa, Y. (eds) Automorphic Forms and Geometry of Algebraic Varieties. (Adv. Stud. Pure Math.,15, vol. pp. 29-40) Amsterdam: North-Holland and Tokyo: Kinokuniya 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. hyperelliptic curve; Lang'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. Galois representation; Serre's conjecture; Hecke character
| 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. hyperplane arrangement; Teroa's conjecture; logarithmic bundles; line arrangement Faenzi, D.; Vallès, J., Logarithmic bundles and line arrangements, an approach via the standard construction, J. Lond. Math. Soc. (2), 90, 675-694, (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. Bogomolov conjecture; height; Beilinson-Bloch conjecture S.W. Zhang, \textit{Gross-Schoen Cycles and Dualising Sheaves}, \textit{Invent. Math.}\textbf{179} 1 [arXiv:0812.0371].
| 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; Mordell-Weil group; Selmer group; Birch and Swinnerton-Dyer conjecture; parity 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. arithmetic transfer conjecture; arithmetic fundamental 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. self-products of varieties; Albanese variety; \(K3\)-surfaces; Bloch's conjecture; zero-cycles; skew zero-cycles; Kummer surface C. Voisin, ''Remarks on zero-cycles on self-products of varieties'' in Moduli of Vector Bundles (Sanda, 1994; Kyoto 1994), Lecture Notes Pure Appl. Math. 179, Dekker, New York, 1996, 265--285.
| 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. cubic curves; elliptic curves; rational points; Mordell'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. Nakai's conjecture; geometric local ring; high order derivations; invariant subrings of regular rings; action of a finite group of automorphisms Ishibashi, Yasunori: Nakai's conjecture for invariant subrings. Hiroshima math. J. 15, No. 2, 429-436 (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. fundamental group; Shafarevich conjecture; absolute Galois group; function field; finite split embedding problem; Abhyankar's conjecture Florian Pop, ``Étale Galois covers of affine smooth curves. The geometric case of a conjecture of Shafarevich. On Abhyankar's conjecture'', Invent. Math.120 (1995) no. 3, p. 555-578
| 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. projective dimension; quadrics; Castelnuovo-Mumford regularity; Stillman's conjecture Huneke, C., Mantero, P., McCullough, J., Seceleanu, A.: A tight bound on the projective dimension of 4 quadrics. J. Pure Appl. Algebra (\textbf{to appear})
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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. semi-abelian analogue of Schanuel's conjecture; linear disjointness; algebraic independence; semi-abelian exponential; generalized semi-abelian logarithm
| 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. norm varieties; norm motives; Bloch-Kato conjecture; chain lemma; norm principle; Rost varieties; Rost motives; norm residue isomorphism theorem; motivic chohomology C. Haesemeyer and C. Weibel, ''Norm varieties and the Chain Lemma (after Markus Rost),'' in Algebraic Topology, New York: Springer-Verlag, 2009, vol. 4, pp. 95-130.
| 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-Kato's reciprocity law; Soulé-Deligne cyclotomic elements; Bloch-Kato 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. algebraic geometry; syzygies; projective normality; normal presentation; higher dimensional varieties with nef canonical bundle; Fujita's conjecture; pluricanonical linear systems on varieties 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. algebraic cycles; rational equivalence; motives; balanced correspondence; generic cycle; minimal field of definition; transcendence degree; Bloch's conjecture; rational curve S. Gorchinskiy, V. Guletskii\?, ``Transcendence degree of zero-cycles and the structure of Chow motives'', Cent. Eur. J. Math., 10:2 (2012), 559 -- 568
| 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. Frey curve; Taniyama-Shimura conjecture; survey; Fermat's Last Theorem; elliptic curves; modular functions; level reduction COX D.: Introduction to Ferma\?s Last Theorem. Amer. Math. Monthly 101 (1994), 3-14.
| 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; rational points; Mordell-Weil group; generator; canonical height; local 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. real algebraic plane curve; Hilbert 16th problem; singularities of plane curve; constructing curves of a given degree; prescribed arrangement; perturbing singular curves with controlled variation of the topology; Ragdale's conjecture Brugallé, E.: Tropical curves, notes from introductary lectures given in July 2013 at Max Planck Institute for Mathematics, Bonn. http://erwan.brugalle.perso.math.cnrs.fr/articles/TropicalBonn/TropicalCurves
| 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. semilinear manifolds; bistellar operations; p.l.-homeomorph; bistellar equivalent; semilinear simplicial sphere; Dehn-Sommerville equations; McMullen's g-conjecture; Schälbarkeit Pachner, U., Konstruktionsmethoden und das kominatorische homoomorphieproblem für triangulationen semilinearer mannigfaltigkeiten, Ahb. Math. Sem. Univ. Hamburg, 57, 69, (1987)
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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 variety; elliptic curve; Mordell-Lang conjecture; Manin-Mumford conjecture; Bogomolov, heights Viada, Evelina, Nondense subsets of varieties in a power of an elliptic curve, Int. Math. Res. Not. IMRN, 1073-7928, 7, 1213-1246, (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. abelian varieties; Hodge conjecture; Weil type; imaginary quadratic field Izadi, Elham, Some remarks on the {H}odge conjecture for abelian varieties, Annali di Matematica Pura ed Applicata. Series IV, 189, 3, 487-495, (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. rationality problem; Noether's problem; multiplicative group actions; monomial automorphisms M. Kang, Y. G. Prokhorov, Rationality of three-dimensional quotients by monomial action, J. Algebra 324 (2010), 2166\ 2197.
| 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. Maxwell's conjecture; zeros of exponential polynomials; zeros of non-negative polynomials; zeros of tropical polynomial DOI: 10.1007/s40598-015-0008-4
| 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; height; Vojta conjecture S.-I. Ih, Height uniformity for algebraic points on curves, Compos. Math. 134 (2002), no. 1, 35-57.
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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 freeness conjecture; log canonical pairs; semi-log canonical pairs; quasi-log structures; log surfaces; stable surfaces; semi-log canonical Fano surfaces; effective very ampleness --------, Effective basepoint-free theorem for semi-log canonical surfaces, Publ. Res. Inst. Math. Sci. 53 (2017), no. 3, 349--370.
| 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. projection onto projective space; embedding; Hartshorne's conjecture; tangent variety; secant variety
| 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; Mordell-Weil rank of elliptic curves Brumer, Armand; McGuinness, Oisín., The behavior of the Mordell-Weil group of elliptic curves, Bull. Amer. Math. Soc. (N.S.), 23, 2, 375-382, (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. Green's conjecture; linear series Clifford index; rational ribbon; resolution Clifford index; canonical curve conjecture D. Eisenbud and M. Green, Clifford indices of ribbons, Trans. Amer. Math. Soc. 347 (1995), no. 3, 757--765.
| 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. Lefschetz trace formula; Deligne's conjecture Varshavsky, Y., \textit{Lefschetz-verdier trace formula and a generalization of a theorem of fujiwara}, Geom. Funct. Anal., 17, 271-319, (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. Bott tower; Bott manifold; toric manifold; Hirzebruch surface; strong cohomological rigidity conjecture; Petrie'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. Parshin's conjecture; Miyaoka-Yau inequality; surfaces of general type; fields of positive characteristic Jang, J, Generically ordinary fibrations and a counterexample to parshin's conjecture, Mich. Math. J., 59, 169-178, (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. elliptic curves over function fields; Mordell-Weil rank; Néron-Tate regulator; Tate-Shafarevich group; \(L\)-function; BSD 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. normed pairing; Galois representations; formal group of finite height; Hilbert's symbol; local field D. G. Benua and S. V. Vostokov, Norm pairing in formal groups and Galois representations, Algebra i Analiz 2 (1990), no. 6, 69 -- 97 (Russian); English transl., Leningrad Math. J. 2 (1991), no. 6, 1221 -- 1249.
| 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 bundles; low-height representations; smooth projective curve; induced bundle; Luna's etale slice 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. elliptic curves; faltings height; Weil 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. algorithm for the computation of the topological type of a real curve; Thom's lemma Roy, M. -F.: Computation of the topology of a real curve. Astérisque 192, 17-33 (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. moving lemma; motivic spaces; Gersten 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; Iwasawa theory; \(p\)-adic heights; \(p\)-adic \(L\)-function; height pairing of abelian varieties; Iwasawa function; rational point of infinite order; Tate duality Karl Rubin, Abelian varieties, \?-adic heights and derivatives, Algebra and number theory (Essen, 1992) de Gruyter, Berlin, 1994, pp. 247 -- 266.
| 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 variety; rational points; linear pencil of projective plane curves; Mordell-Weil lattices; Manin-Shafarevich theorem; height pairing; Lefschetz pencils of hyperplane sections Shioda, T.: Generalization of a theorem of Manin-Shafarevich. Proc. Japan acad. 69A, 10-12 (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. p-adic fields; Kochen operator; finite field; Merckel's lemma; constructive proof
| 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 manifold; entire curves; jet differentials; Green-Griffiths conjecture; Kobayashi's conjecture; hypersurfaces Simone Diverio, Joël Merker & Erwan Rousseau, ''Effective algebraic degeneracy'', Invent. Math.180 (2010) no. 1, p. 161-223
| 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. isotriviality; effective Mordell; semiabelian variety; positive characteristic; survey of diophantine geometry; bounding the heights of rational points on curves over function fields; semiabelian varieties; Roth's theorem Voloch, José Felipe, Diophantine geometry in characteristic \(p\): a survey.Arithmetic geometry, Cortona, 1994, Sympos. Math., XXXVII, 260-278, (1997), Cambridge Univ. Press, Cambridge
| 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. global field of positive characteristic; Langlands conjecture; \(\ell\)-adic representations; Weil group; automorphic cuspidal representations; adele , Two dimensional /-adic representations of the Galois group of a global field of characteristic/? and automorphic forms on GL(2), J. Soviet Math., 36, No. 1 (1987), 93-105.
| 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. numerical effective bundle; higher dimensional analogue of Mordell's finiteness conjecture over function fields; nef
| 0 |
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