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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. connected reductive linear algebraic group; variety of Borel subgroups; Lie algebra; Weil conjecture; Frobenius endomorphism; \(\ell \)-adic cohomology group; eigenvalues Springer, T.A.: A purity result for fixed point varieties in flag manifolds. J.~Fac.~Sci.~Univ.~Tokyo Sect.~IA, Math.~\textbf{31}, 271-282 (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. higher algebraic \(K\)-theory; Milnor \(K\)-theory; finite fields; Tate's conjecture; Beilinson's conjecture; Parshin's conjecture; Chow groups; category of pure motives; étale cohomology; motivic cohomology Thomas Geisser, ``Tate's conjecture, algebraic cycles and rational \(K\)-theory in characteristic \(p\).'', \(K\)-Theory13 (1998) no. 2, p. 109-122
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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. construction of elliptic curves from automorphic Hecke newforms; Drinfeld modular curves; Shimura-Taniyama-Weil conjecture; Jacobian; strong Weil curve; strong Weil uniformization Gekeler, E-U; Reversat, M, Jacobians of Drinfeld modular curves, J. für die reine und angewandte Mathematik, 476, 27-93, (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. blowing up; nef; Szemberg conjecture; Nagata's conjecture Harbourne B.: Seshadri constants and very ample divisors on algebraic surfaces. J. Reine Angew. Math. 559, 115--122 (2003)
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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. Batyrev-Manin conjecture; height; Kummer surface; rational points
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. generalized Weil's reciprocity law; one-dimensional group variety; topology of the fiber-structure; invariant of homomorphism; Riemann 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. cyclotomic unit; arithmetic of an elliptic curve; Mordell-Weil group; Tate-Shafarevich group; Birch and Swinnerton-Dyer conjecture; Weil curves; Selmer group; family of Heegner points; elliptic units V. A. KOLYVAGIN, The Mordell-Weil and Shafarevich-Tate groups for Weil elliptic curves. (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 52, no. 6 (1988), pp. 1154-1180, 1327; translation in Math. USSR-Izv., 33, no. 3 (1989), pp. 473-499. Zbl0681.14016 MR984214
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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. 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. group of rational points; Mazur's conjecture; commutative algebraic group; density property; linear groups; abelian varieties; extensions of an elliptic curve Waldschmidt, M.: Densité des points rationnels sur un groupe algébrique. Experiment. Math., 3, pp. 329--352 (1994) (Erratum: vol. 4 (3) 1995), 255)
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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. De Rham cohomology; crystalline action of Weil group; Morita's \(p\)-adic gamma function; absolute Hodge cycles; Frobenius matrix of Fermat curves Ogus, A, A \(p\)-adic analogue of the chowla-Selberg formula, \(p\)-adic analysis (Trento, 1989), Lect. Notes Math., 1454, 319-341, (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. Newman's conjecture; zeros of the Riemann zeta function; \(L\)-functions; function fields; random matrix theory; Sato-Tate conjecture Andrade, J.; Chang, A.; Miller, S. J.: Newman's conjecture in various settings. J. number theory 144, 70-91 (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. elliptic curve over a global function field; Mordell-Weil lattices; determinants; cycle-class map; crystalline cohomology; height pairing [3] N. Dummigan, `` The determinants of certain Mordell-Weil lattices {'', \(Amer. J. Math.\)117 (1995), no. 6, p. 1409-1429. &MR 13 | &Zbl 0914.}
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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. Rumely's theorem; Zhang's arithmetic ampleness theorem; Bost's extension of Arakelov geometry; integral points; arithmetic surfaces; heights; generalization of the Fekete-Szegő theorem [2] Autissier (P.).-- Points entiers sur les surfaces arithmétiques, Journal für die reine und angewandte Mathematik 531, 201-235 (2001). &MR~18 | &Zbl~1007.
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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. variation of the canonical height; elliptic curve; real-valued Weil height function; Tate height Holmes, D.: Néron models of jacobians over base schemes of dimension greater than 1. J. Reine Angew. Math. http://arxiv.org/abs/1402.0647 (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. Igusa's conjecture; exponential sums; non-degenerate polynomials
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Noether's problem; rationality problem; multiplicative invariant field; unramified Brauer group; Bogomolov multiplier; unramified cohomology group
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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; exceptional set; minimal model program
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. quadratic bundle; Manin's conjecture; accumulating subvariety Elsenhans, A-S, Rational points on some Fano quadratic bundles, Exp. Math., 20, 373-379, (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. Norm variety; motivic cohomology; Bloch-Kato conjecture; chain lemma; Milnor \(K\)-theory A.\ A. Suslin and S. Joukhovitski, Norm varieties, J. Pure Appl. Algebra 206 (2006), no. 1-2, 245-276.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Weil height; projective points; finiteness
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. exterior Galois representations; fundamental groups of punctured elliptic curves; Grothendieck's anabelian conjecture Cadoret, A., Tamagawa, A.: On subgroups of \({GL}_r(\mathbb{F}_l)\) and representations of étale fundamental groups. Preprint. http://www.math.polytechnique.fr/~cadoret/Travaux.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. algebraic cycles; etale topology; Homotopy; homology; Chow groups; Bejlinson's conjectures; regulator map; Lichtenbaum's conjectures; Milnor K-groups; Soulé's conjecture; poles of the zeta function Bloch, Spencer, Algebraic cycles and the {B}eĭlinson conjectures, The {L}efschetz Centennial Conference, {P}art {I} ({M}exico {C}ity, 1984), Contemp. Math., 58, 65-79, (1986), Amer. Math. Soc., Providence, RI
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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; Manin's conjecture; universal torsor parameterizations; lattice point counting Pieropan, M.: On the unirationality of del Pezzo surfaces over an arbitrary field
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. non-commutative resolution; Springer resolution; non-commutative desingularization; determinantal variety; Young diagram; Young quiver; resolution of determinantal variety; Orlov's conjecture; tilting module
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. minimal models of families of threefolds; Mori theory; deformation families; terminal singularities; flips for families; small contractions; Reid's conjecture J. Kollár and S. Mori, Classification of three-dimensional flips, J. Amer. Math. Soc. 5 (1992), no. 3, 533-703.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. \(K3\) surface; Hasse-Weil zeta function; complex multiplication; good reduction; Tate 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. 3-rank of the class group of an imaginary quadratic field; descent elliptic curve; Shimura's correspondence; Birch and Swinnerton-Dyer conjecture Jan Nekovář, Class numbers of quadratic fields and Shimura's correspondence, Math. Ann. 287 (1990), no. 4, 577 -- 594.
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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. étale cohomology; Weil II; Ultraproduct coefficients; compatible families and motives; Langlands correspondence; companion conjecture; Cebotarev density 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. primitive roots; Artin's conjecture; function field; Dirichlet density of prime ideals Clark, D. A.; Kuwata, M.: Generalized Artin's conjecture for primitive roots and cyclicity mod p of elliptic curves over function fields. Canad. math. Bull. 38, No. 2, 167-173 (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. modular curves; survey; Taniyama conjecture; Fermat's last theorem
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. abelian varieties; Mordell-Weil group; degree; height D.W. Masser, Specializations of finitely generated subgroups of abelian varieties , Trans. Amer. Math. Soc. 311 (1989), 413-424. 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. graded Betti numbers; Green's conjecture; space curve; plane algebraic curve Loose, F, On the graded Betti numbers of plane algebraic curves, Manuscr. Math., 64, 503-514, (1989)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow ring; motives; Bloch-Beilinson filtration; hyperkähler variety; Lagrangian subvariety; constant cycle subvariety; (Hilbert scheme of) \(K3\) surface; Beauville's splitting property; multiplicative Chow-Künneth decomposition; spread of algebraic 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. Getzler's cohomological relation; moduli space of 4 pointed elliptic curves; elliptic Gromov-Witten invariants; Virasoro conjecture Pandharipande, R., A geometric construction of Getzler's elliptic relation. Math. Ann., 313 (1999), 715--729.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. del Pezzo surfaces; rational points; Manin's conjecture; Peyre's constant; lattice points; Picard group; divisor problems; binary forms R. De la Bretèche and T. D. Browning, Manin's conjecture for quartic del Pezzo surfaces with a conic fibration, Duke Math. J. 160 (2011), no. 1, 1 -- 69.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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 geometry; dual variety; singularities; multisecant spaces; Bertini theorem; Zak'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. exponential sums; Igusa's conjecture; Igusa's local zeta functions; motivic oscillation index; non-rational singularities; analytic isomorphism of singularities
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Brauer group; Gersten's conjecture; local-global principle
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. o-minimality; André-Oort conjecture; Siegel modular varieties Y. Peterzil and S. Starchenko, Definability of restricted theta functions and families of abelian varieties, Duke J. Math. 162 (2013), 731-765.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Hecke characters of imaginary quadratic fields; weak Leopoldt's conjecture Bars, The weak Leopoldt's conjecture for Hecke characters of imaginary quadratic fields, J. Algebra 319 pp 1954-- (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. Birch-Swinnerton-Dyer conjecture; Hasse-Weil conjecture; Shimura- Tamagawa-Weil conjecture; algorithm for computing the Mordell-Weil group of an elliptic curve Josef Gebel and Horst G. Zimmer, Computing the Mordell-Weil group of an elliptic curve over \?, Elliptic curves and related topics, CRM Proc. Lecture Notes, vol. 4, Amer. Math. Soc., Providence, RI, 1994, pp. 61 -- 83.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. vector bundles on curves; coherent systems; moduli space of coherent systems; stable bundle; Brill-Noether theory of vector bundles; Butler'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. Quillen K-groups; Chow groups; zeta function of varieties over finite field; étale cohomology groups; crystalline cohomology groups; Tate's conjecture James Stuart Milne, ``Values of zeta functions of varieties over finite fields'', Am. J. Math.108 (1986) no. 2, p. 297-360
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic curve; Green's conjecture; anticanonical surface; minimal free resolution Lelli-Chiesa, Margherita, Green's conjecture for curves on rational surfaces with an anticanonical pencil, Math. Z., 275, 3-4, 899-910, (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. Arveson's resistant conjecture; graded Hilbert module; d-shift Hilbert module; essentially normal; stable division property; ring of polynomials O. M.SHALIT,\textit{Stable polynomial division and essential normality of graded Hilbert modules}, J. Lond. Math. Soc. (2) 83 (2011), no. 2, 273--289. http://dx.doi.org/10.1112/jlms/jdq054.MR2776637
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. zero cycles; Bloch's conjecture; \(K3\) surfaces C. Voisin, Symplectic involutions of \(K3\) surfaces act trivially on \(CH_{0}\), Doc. Math. 17 (2012), 851--860.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. congruent number problem; Hasse-Weil \(L\)-function; elliptic curves; modular forms; integral weight; half-integral weight; Fourier expansion; Hecke operators; Shimura lift; Waldspurger's theorem N. Koblitz, \textit{Introduction to elliptic curves and modular forms}, 2\^{}\{nd\} edition, Springer, Germany (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. elliptic curve; Mordell-Weil group; generators; height 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. nodal curve; Bell polynomial; Enriques diagram; Hilbert scheme; Göttsche's conjecture; quintic threefold; abelian surfac S.\ L. Kleiman and R. Piene, Node polynomials for families: Methods and applications, Math. Nachr. 271 (2004), 69-90.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. index theorem; analytic torsion; heat kernel of the Laplacian on Riemann manifolds; Arakelov's theory; hermitean bundles; Mordell conjecture; arithmetic intersection theory for general arithmetic varieties; arithmetic Riemann-Roch theory; arithmetic Chern classes; arithmetic \(K\)- groups; arithmetic Chow groups; Dirac operators on compact Kähler manifolds; super-Dirac operators [15] Faltings (G.).-- Lectures on the arithmetic Riemann-Roch theorem, Annals of Math. Studies, vol. 127, Princeton University Press, 1992. &MR~11 | &Zbl~0744.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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 an imaginary quadratic field; Selmer\(groups\); Weil curve; Heegner points; conjecture of Birch and Swinnerton-Dyer
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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; integrable metrized line bundles; normalized height Zhang, S., \textit{small points and adelic metrics}, J. Alg. Geom., 4, 281-300, (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. Lehmer problem; Néron-Tate; canonical height; elliptic curves; complex multiplication; Arakelov geometry; arithmetic intersection; Dirichlet L-functions; Faltings 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. del Pezzo surface; rational points; restricted divisor problem; conic bundle; Manin's conjecture doi:10.1112/jlms/jds017
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. canonical ring of 1-connected curves; Miles Reid's 1-2-3 conjecture K. KONNO, 1-2-3 theorem for curves on algebraic surface, J. reine. angew. Math., 533 (2001), pp. 171-205. Zbl0965.14004 MR1823868
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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. Kobayashi hyperbolic space; Lang's conjecture; rational point; finiteness 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. Guth-Katz joints; Carbery's conjecture
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. height; size; house; projective length; arithmetic geometry; projective variety; approximation measure; \(p\)-adic integration; local heights; Chow forms Philippon P.: Sur des hauteurs alternatives, II. Ann. Inst. Fourier, Grenoble 44(2), 1043--1065 (1994)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Diophantine approximation; arithmetic function field; Roth's theorem; Thue-Siegel method
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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. Tautological ring; Faber's conjecture; socle; Feynman move Petersen, D.: Cohomology of local systems on loci of \(d\)-elliptic abelian surfaces. Mich. Math. J. (to appear). Preprint (2010). arXiv:1004.5462
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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. global field of positive characteristic; Langlands conjecture; \(\ell\)-adic representations; Weil group; automorphic cuspidal representations; adele V. G. Drinfel\(^{\prime}\)d, Two-dimensional \?-adic representations of the Galois group of a global field of characteristic \? and automorphic forms on \?\?(2), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 134 (1984), 138 -- 156 (Russian, with English summary). Automorphic functions and number theory, II.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. rational points of bounded degree on a curve; Faltings' theorem; Mordell's conjecture; Brill-Noether loci; Jacobian
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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 and abelian varieties over finite fields; distribution of the trace of matrices; equidistribution; Frobenius operator; generalized Sato-Tate conjecture; Katz-Sarnak theory; random matrices; Weyl's integration 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. symbolic powers; Waldschmidt constant; Chudnovsky's conjecture; containment problem; ideals of points; stable Harbourne 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. Zariski's main lemma on holomorphic functions; Artin-Rees theorem; Whitney stratification; singular loci O'carroll, Liam: A uniform Artin--Rees theorem and Zariski's Main lemma on holomorphic functions. Invent. math. 90, No. 3, 647-652 (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. geometric Bogomolov conjecture; non-Archimedean geometry; canonical measures K. Yamaki, Strict support of canonical measures and applications to the geometric Bogomolov conjecture, Compos. Math. (2015), 10.1112/S0010437X15007721.
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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. submanifolds with ample normal bundle; \(\mathbb{P}^ 1\)-bundles; \(\mathbb{P}^ m\)-bundles; Hartshorne'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. \(p\)-adic deformation; algebraic cycles; crystalline Chern character; de Rham cohomology; Hodge filtration; de Rham-Witt complex; Grothendieck's variational Hodge conjecture; Fontaine-Messing's \(p\)-adic variational Hodge conjecture; motivic pro-complex; Suslin-Voevodsky motivic complex; Fontaine-Messing-Kato syntomic complex; fundamental triangle; crystalline Hodge obstruction; topological cyclic homological theory; Milnor \(K\)-theory Bloch, S.; Esnault, H.; Kerz, M., \textit{p}-adic deformation of algebraic cycle classes, Invent. Math., (2013)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. adjoint linear system; local cohomology; Fujita's freeness conjecture; ample invertible sheaf Smith, K. E.: Fujita's freeness conjecture in terms of local cohomology. J. algebraic geom. 6, 417-429 (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. cell decomposition of modular varieties; Siegel modular group; Voronoi's reduction theory; analytic Whitney-stratification; Poincaré dual decomposition; Voronoi cells; Satake partial compactification MacPherson, R.; McConnell, M., Explicit reduction theory for Siegel modular threefolds, Invent. math., 111, 575-625, (1993)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Wahl's conjecture; Frobenius splitting; maximal multiplicity Lauritzen, N., Thomsen, J.F.: Maximal compatible splitting and diagonals of Kempf varieties. Ann. Inst. Fourier (Grenoble) \textbf{61} (2011), vol. 6, 2543-2575 (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. elliptic functions; \(L\)-series; complex multiplication; \(p\)-adic uniformization; modular functions; Mordell-Weil theorem for function fields; canonical height; Néron-model; minimal model J.H. Silverman, in \(Advanced Topics in The Arithmetic of Elliptic Curves\), Graduate Texts in Mathematics, vol. 151 (Springer, New York, 1994)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. elliptic surface; canonical height; Weil height 10.1006/jnth.1994.1070
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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 over function fields; theorem of the kernel . Coleman, R.F. , '' Manin's proof of the Mordell conjecture over function fields '', preprint.
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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. chromatic polynomial; Read'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. deformation functor; Galois cohomology; Galois representation; Shimura-Taniyama-Weil conjecture; \({\mathbb F}_p\)-representation; finite flat group schemes Conrad, B., \textit{the flat deformation functor}, Modular forms and Fermat's last theorem (Boston, MA, 1995), 373-420, (1997), Springer, New York
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow groups; motives; hyperkähler varieties; anti-symplectic involution; \(K3\) surfaces; (double) EPW sextics; Beauville's splitting principle; multiplicative Chow-Kenneth decomposition; spread of algebraic 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. topology of complex polynomial; critical points; critical values; bouquet of spheres; atypical values from infinity; tame polynomials; Whitney stratification; frontier condition; Thom-Mather first isotopy theorem; Ehresmann'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. abelian variety; absolute endomorphism ring; Weil height; Jacobian Masser, D, Specialization of endomorphism rings of abelian varieties, Bull. Soc. Math. Fr., 124, 457-476, (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 scheme of a surface; vanishing theorem; Le Potier's strange duality conjecture; cohomology Danila, G, Sur la cohomologie d'un fibré tautologique sur le schéma de Hilbert d'une surface, J. Algebraic Geom., 10, 247-280, (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. Bibliography; geometric invariant theory; rationality of the field of invariants; constructive invariant theory; Hilbert's 14th problem; Poincaré series; categorical quotients; Russian conjecture É. B. Vinberg and V. L. Popov, ''Invariant Theory,'' in Algebraic Geometry-4, Itogi Nauki i Tekhniki, Ser. Sovrem. Probl. Mat., Fund. Napr., 55 (Moscow, VINITI, 1989), pp. 137--309.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. resolution of surface singularities; triple section surface; target point; triple covering; inner double points; Durfee's conjecture; two- dimensional hypersurface singularities of multiplicity 3; Milnor number; simple elliptic singularity Némethi, A.: Dedekind sums and the signature of \(f(x,y)+z^N\). Selecta. Math. (N.S.) \textbf{4}(2), 361-376 (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. set of points in projective space; syzygies of quadrics; rational normal scroll; strong Castelnuovo lemma; minimal resolution conjecture DOI: 10.1007/BF02571888
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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-Siegel conjecture; differential equations for G-functions; Picard- Fuchs equations; Padé approximations; accessory parameters; transcendence; elliptic curves; continued fractions; fast computation of \(\pi \) D.V. Chudnovsky and G.V. Chudnovsky. Computational problems in arithmetic of linear differential equations. Some Diophantine applications. Number theory (New York, 1985/1988), 12--49, Lecture Notes in Math., 1383, Springer, Berlin (1989).
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. quasi homogeneous varieties; quantum cohomology; Dubrovin'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. asymptotic commutative algebra; linear coordinate transformations; Stillman's conjecture; twisted commutative algebras; Zariski-topology
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. effective Chabauty; cardinality of rational points on a curve; Fermat's Last Theorem; rank of the Mordell-Weil group; Fermat curve; rational points on curves W. G. McCallum, ''On the method of Coleman and Chabauty,'' Math. Ann., vol. 299, iss. 3, pp. 565-596, 1994.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Galkin's conjecture; property \(\mathcal{O}\); gamma conjectures
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. polylogarithms; Beilinson's conjecture; Shimura varieties; mixed Shimura varieties; Hodge structures; mixed sheaves; Tannakian categories; \(L\)-functions J. Wildeshaus, \textit{Realizations of Polylogarithms}, Springer, \textit{Lect. Notes Math.}\textbf{1650} (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. Rationality; Noether's problem; Multiplicative actions; Algebraic tori Kang, M., Rationality problem of \(G L_4\) group actions, Adv. Math., 181, 321-352, (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. faithful one-dimensional representation; Stark's conjectures; Lichtenbaum's conjecture; \(L\)-functions; Chinburg'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. Campana point; Vojta's conjecture; abelian variety; level structure
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Chow group; Bloch's conjecture; Godeaux surface; algebraic cycles Voisin, Claire, Sur les zéro-cycles de certaines hypersurfaces munies d'un automorphisme, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 19, 4, 473-492, (1992)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Macaulayfication; dualizing complex; \(p\)-standard system of parameters; \(d\)-sequence; Sharp's conjecture; blowing-up; Cohen-Macaulay scheme; desingularization; Noetherian scheme T. Kawasaki, ''On Macaulayfication of Noetherian schemes,'' Trans. Amer. Math. Soc., 352, No. 6, 2517--2552 (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. elliptic curve with complex multiplication; Mordell-Weil group; p-adic height function D. Bertrand, Relations d'orthogonalité sur les groupes de Mordell-Weil , Séminaire de théorie des nombres, Paris 1984-85, Progr. Math., vol. 63, Birkhäuser Boston, Boston, MA, 1986, pp. 33-39.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Atiyah-Segal map; Riemann-Roch transformation; Grothendieck-Riemann-Roch theorem; Deligne-Mumford stack; quotient stack; inertia stack; equivariant $K$-theory; higher Chow groups; coarse moduli space map; Morita isomorphism; Köck'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. Birch and Swinnerton-Dyer conjecture; global function fields; Weil-étale 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. Göttsche's conjecture; Göttsche-Yau-Zaslow Formula; quasimodular forms; algebraic cobordism group; degeneration Tzeng, Y.-J., A proof of the Göttsche-Yau-Zaslow formula, J. Differ. Geom., 90, 439-472, (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. Bridgeland stability conditions; Bogomolov-Gieseker inequalities; Fujita's conjecture Bayer, A; Bertram, A; Macrì, E; Toda, Y, Bridgeland stability conditions on threefolds II: an application to fujita's conjecture, J. Algebraic Geom., 23, 693-710, (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. canonical surfaces; canonical map; canonical divisor; birational map; Reid's conjecture; Del Pezzo surface
| 0 |
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