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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 curves; integral points; Siegel's theorem Alvanos, P.; Bilu, Y.; Poulakis, D., \textit{characterizing algebraic curves with infinitely many integral points}, Int. J. Number Theory, 5, 585-590, (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. Eisenstein series; Hecke eigensheaf; Hecke property; geometric Langlands correspondence; Drinfeld's conjecture; Drinfeld's compactifications; space of deformations; IC sheaves; Koszul complex; Koszul duality; deforming local systems; extension by zero Braverman, A.; Gaitsgory, D., \textit{deformations of local systems and Eisenstein series}, Geom. Funct. Anal., 17, 1788-1850, (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. Alexandrov's conjecture; Kontsevich-Witten-Hodge tau-functions
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. lemniscatic sine function; lattice of periods; Riemann surface of genus \(1\); angle addition formulas for lemniscatic functions; constructible number; Abel's result Joel Langer and David Singer, The lemniscatic chessboard, Forum Geometricorum, Vol. 11 (2011), 183--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. superanalogy of Beilinson-Bernstein's theory; twisted \({\mathcal D}\)-modules on flag manifolds; Borel-Weil-Bott I. Penkov and I. Skornyakov, Cohomologie des {\mathcal{D}}-modules tordus typiques sur les supervariétés de drapeaux, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 20, 1005-1008.
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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. \(p\)-adic Dwork cohomology; Katz conjecture; exponential modules; twisted de Rham theory; zeta function of the complete intersection; Weil conjectures; characteristic polynomial; Newton polygon; Hodge polygon; hypersurfaces; middle-dimensional cohomology Adolphson, A.; Sperber, S., On the zeta function of a complete intersection, Ann. Sci École Norm. Sup., 4, 287-328, (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. elliptic curve; logarithmic Weil height; isogeny Masser, D. W.; Wüstholz, G., Estimating isogenies on elliptic curves, Invent. Math., 100, 1, 1-24, (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. Manin conjecture; height zeta-function; canonical height; toric 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. Green's conjecture; canonical curves; syzygies; rational normal curves; tangent developable 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. \(p\)-adic integral of a complex power function; Igusa's conjecture; generalized Igusa local zeta functions
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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. infinite fields; vector spaces; Procesi's conjecture; invariants of several matrices A.N. Zubkov.: Endomorphisms of tensor products of exterior powers and Procesi hypothesis. Commun. Algebra 22, 6385--6399 (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. Siegel's theorem; affine curves; integral points; Roth's theorem; nonstandard analysis
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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 structure; moduli space; Weil-Petersson form; Siegel form
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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 motives and their \(L\)-functions; local height pairings; algebraic cycles; Chow groups; mixed motives; period mapping; global height pairing; Birch-Swinnerton-Dyer-Beilinson-Bloch conjecture; critical value conjectures A. J. Scholl, ''Height pairings and special values of \(L\)-functions,'' in Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math. 55, Amer. Math. Soc., Providence, 1994, 571--598.
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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. Calabi-Yau threefold; Clemen's conjecture; étale double covering; rigid
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. functional equations; Deligne's irregular Hodge theory; Siegel's theorem; Siegel-Shidlovsky 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. conjecture of Lang and Silverman; absolute height; abelian surfaces; local height Pazuki, F., \textit{minoration de la hauteur de Néron-Tate sur LES surfaces abéliennes}, Manuscripta Math., 142, 61-99, (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 curves over an algebraic number field; Galois module of \(p\)-torsion points; height conjecture; asymptotic Fermat conjecture; principally polarized abelian variety; curves of genus 2 G. Frey, On elliptic curves with isomorphic torsion structures and corresponding curves of genus 2, in Elliptic curves, modular forms, \& Fermat's last theorem (Hong Kong, 1993), Internat. Press, Cambridge, MA, 1995, pp. 79--98.
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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 representation; Taniyama-Weil conjecture; semi-stable elliptic curves over \(\mathbb{Q}\)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. quantum cohomology; orbi-curve; 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. Serre's conjecture II; semisimple algebraic groups
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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. Suita conjecture; complex torus; Bergman kernel; Arakelov-Green's 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. transcendence; zero estimates; algebraic independence; Baker's theory; algebraic groups; Neron-Tate height; Abelian variety; exponential function; Weierstrass elliptic function; linear forms in logarithms D. W. Masser, ``Zero estimates on group varieties'' in Proceedings of the International Congress of Mathematicians, Vols. 1-2 (Warsaw, 1983) , PWN, Warsaw, 1984, 493-502.
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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. values at integer points of \(L\)-functions; crystalline representation; de Rham representation; periods; regulators; Tamagawa number for motives; motivic pair; Tate-Shafarevich group; Beilinson's conjecture on the regulator map S. Bloch and K. Kato, \textit{L}-functions and Tamagawa numbers of motives, The Grothendieck Festschrift, vol. 1, Progr. Math. 86, Birkhäuser, Boston (1990), 333-400.
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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. resolution of singularities, hypersurfaces; complex analytic spaces; infinitely near singularities; modifications; horizontal morphisms, vertical morphisms, cone-fibered spaces, blow-ups, blowing cones, normal cones; tangent cones; Weierstrass preparation theorem; normal flatness; maximal contact; idealistic exponents; characteristic cones; continuity of maximal contact; contact stability theorems; trees; forests; groves; polygroves; soil; gardens; allées; normal crossings; Samuel stratification; complex analytic foliations; valuations; Newton polygon; Thom'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. dimension growth conjecture; rational points of bounded 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. Hermitian lattice; order in quadratic field; isogeny class; polarization; curves with many points over finite fields; Siegel modular form; theta constant; theta null point; algorithm; Igusa modular form; Serre's obstruction; Schottky locus
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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; King's conjecture; exceptional collection; Frobenius splitting Costa L., Miró-Roig R.M., Frobenius splitting and Derived category of toric varieties, Illinois J. Math., 2010, 54(2), 649--669
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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. control theorems; Shimura-Taniyama-Weil conjecture; elliptic curve; modular curve; deformation rings; Hecke algebras; modular Galois representations; moduli spaces of elliptic curves; modular forms; Abelian \(\mathbb{Q}\)-curves Hida, H.: Geometric Modular Forms and Elliptic Curves, 2nd edn. World Scientific, Singapore (2012)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. rational points; abelian ramified covers on curves; weil heights on commutative group schemes; Fermat last theorem M. L. BROWN , Endomorphisms of Group Schemes and Rational Points on Curves (Bull. Soc. Math. France, Vol. 115, 1987 , pp. 1-17). Numdam | MR 88h:11040 | Zbl 0628.14017
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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. unlikely intersections; multiplicative groups; Zilber conjecture; Manin-Mumford conjecture; elliptic surfaces; problems of Masser; Andre-Oort conjecture U. Zannier, \(Some Problems of Unlikely Intersections in Arithmetic and Geometry (with Appendixes by D. Masser)\). Annals of Mathematics Studies, vol. 181 (Princeton University Press, Princeton, 2012)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Hodge conjecture for abelian varieties; abelian varieties of Weil type; Mumford-Tate groups; abelian variety of Weil type; abelian fourfolds; exceptional Hodge classes van Geemen B.: An introduction to the Hodge conjecture for abelian varieties, Algebraic cycles and Hodge theory, Torino 1993, Lecture Notes in Math., vol. 1594, pp. 233--252. Springer (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. abelian threefold; Jacobian; Klein's formula; Siegel modular forms; Teichmüller modular forms Lachaud G., Ritzenthaler C., Zykin A.: Jacobians among Abelian threefolds: a formula of Klein and a question of Serre. Math. Res. Lett. 17(2), 323--333 (2010)
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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. Gröbner bases; syzygies; resolution of singularities; monodromy; Brieskorn lattice; Tate resolution; cohomology of coherent sheaves; Beilinson monads; invariant rings; binary forms; Green's conjecture; construction of canonical curves Schreyer, F.O.: Some topics in computational algebraic geometry. In: Conference Proceedings of 'Advances in Algebra and Geometry, Hyderabad 2001, pp. 263--278 (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. elementary proof of Dyson's lemma; intersection theory; Schmidt subspace theorem M. Nakamaye , Intersection Theory and Diophantine Approximation. to appear , Journal of Algebraic Geometry. MR 1658224 | Zbl 0953.11026
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. abelian varieties; normalised height; Lehmer problem
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. moduli of algebraic curves; moduli of Riemann surfaces; mapping class groups; homological stability; Mumford's conjecture; Madsen-Weiss theorem Wahl, N.: The Mumford conjecture, madsen-Weiss and homological stability for mapping class groups of surfaces. IAS/park city math. Ser. 20, 109-138 (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. Dyson's theorem; integral points on curves; Siegel's theorem; diophantine approximation on curves
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Siegel's theorem; Siegel family; braid action on covers; Hurwitz spaces; unirationality criterion; rational functions; Hilbert's irreducibility theorem; exceptional polynomials P. Dèbes and M. Fried,Integral specialization of families of rational functions, Pacific Journal of Mathematics190 (1999), 45--85.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Lang conjecture; meet of algebraic subvariety and linear torus; linear form with algebraic coefficients; generalization of Thue-Siegel-Roth theorem; exponential diophantine equation; commutative algebraic group; finite union of subsets Laurent, M.: Exponential Diophantine equations. C. R. Acad. sci. Paris, ser. I 296, 945-947 (1983)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. generic syzygy varieties; vector bundles; curves of genus 7; Green's conjecture Eusen F and Schreyer F -O, \textit{A remark on a conjecture of Paranjape and Ramanan, in: Geometry and arithmetic, EMS Ser. Congr. Rep.} (2012) (Zürich: Eur. Math. Soc.) pp. 113-123
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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. Gröbner bases; Gröbner rings; Gröbner ring conjecture; valuation rings with zero-divisors; Krull dimension; Buchberger's algorithm Monceur, S.; Yengui, I., On the leading terms ideal of polynomial ideal over a valuation ring, J. algebra, 351, 382-389, (2012)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. modular curves; Ribet's isogeny; Ogg's conjecture; Eisenstein ideal; cuspidal divisor group
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. discrete logarithm problem in finite fields; discrete logarithm problem on elliptic curves over finite fields; Weil's pairing
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. evaluation of L-series; Heegner points on elliptic curves; Birch-Stephens conjecture; Tate height of the canonical rational points B. J. Birch and N. M. Stephens, ''Computation of Heegner points,'' in Modular Forms, Chichester: Horwood, 1984, pp. 13-41.
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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. minimal model program; Shokurov's ACC conjecture; semi-continuity of discrepancy Kawakita, Masayuki, Ideal-adic semi-continuity of minimal log discrepancies on surfaces, Michigan Math. J., 62, 2, 443-447, (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. Tate-Shafarevich group; Mordell-Weil theorem; descent; elliptic Iwasawa theory; Selmer group; survey; Birch-Swinnerton-Dyer conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Q-curve; abelian variety of GL(2)-type; Serre's conjecture T. Yamauchi, \(\ACHIQ\)-motives and modular forms , Journal of Number Theory 128 (2008), 1485-1505.
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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. Chevalley-Weil theorem; étale cover; specializations; class groups of number fields; Hilbert's irreducibility 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. Riemann zeta function; special value; Euler'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. line arrangements; free arrangements; Terao's conjecture Vallès, J., Freeness of line arrangements
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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 rigid Calabi-Yau threefolds; Tate's conjecture; modular forms of weight 4 and level 8 Cynk S., Meyer C.: Modular Calabi--Yau threefolds of level eight. Int. J. Math. 18(3), 331--347 (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. defective threefold; multi-projective space; zero-dimensional schemes; Terracini's lemma Catalisano, M. V.; Geramita, A. V.; Gimigliano, A., Segre-Veronese embeddings of \(\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1\) and their secant varieties, Collect. Math., 58, 1, 1-24, (2007), MR 2310544 (2008f:14069)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. matroid; independent set; Mason's conjecture; Lorentzian polynomial; Hodge-Riemann relation; morphism of matroids
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. crystalline cohomology of modular curves; étale cohomology; \(p\)-divisible group; Shimura curve; Fontaine's conjecture Faltings, Gerd, Crystalline cohomology of semistable curve\textemdash the \({\mathbf Q}_p\)-theory, J. Algebraic Geom., 1056-3911, 6, 1, 1\textendash 18 pp., (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. homogeneous hypersurfaces with line singularities; deformations with constant Lê numbers; topological \(\mathcal V\)-equisingularity; equimultiplicity; Thom's \(a_f\) condition; Zariski's multiplicity 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. multiplicity of a root of an algebraic equation; multiplicity of a point of an algebraic variety; intersection multiplicity of algebraic varieties at a point; Weil's multiplicity; Hilbert-Samuel's multiplicity
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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. general linear supergroup; Borel-Weil-Bott theorem; Kempf's vanishing theorem A. N. Zubkov, \textit{Some homological properties of} GL(\(m\)|\(n\)) \textit{in arbitrary characteristic}, J. Algebra Appl. \textbf{15} (2016), no. 7, 1650119, 26 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. Mordell-Weil group; Néron-Severi group of an elliptic surface; intersection theory; Mordell-Weil lattice of an elliptic surface; height pairing Tetsuji Shioda, ``On the Mordell-Weil lattices'', Comment. Math. Univ. St. Pauli39 (1990) no. 2, p. 211-240
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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. absolute Galois groups; Grothendieck's anabelian conjecture; function field; birational geometry
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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. general blowing-up of the projective plane; Alexander's conjecture Stéphane Chauvin and Cindy De Volder, Some very ample and base point free linear systems on generic rational surfaces, Math. Nachr. 245 (2002), 45 -- 66. , https://doi.org/10.1002/1522-2616(200211)245:13.0.CO;2-L
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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. specialization; algebraic covers; twisting lemma; Hilbert's irreducibility theorem; Grunwald's problem; PAC fields; local fields; global fields; Hurwitz spaces Dèbes, Pierre and Legrand, François Specialization results in Galois theory Trans. Amer. Math. Soc.365 (2013) 5259--5275 Math Reviews MR3074373
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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. polarized \(K3\) surfaces; Tate's conjecture for \(K3\) surfaces; finitely generated fields of odd characteristic; Kuga-Satake abelian varieties Madapusi Pera, K., \textit{the Tate conjecture for K3 surfaces in odd characteristic}, Invent. Math., 201, 625-668, (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. \(p\)-adic periods for reductive groups; Tamagawa measures; Tamagawa numbers; Tamagawa number conjecture for tori A. Huber and G. Kings, A cohomological Tamagawa number formula, to appear Nagoya Math. J.
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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. semipositivity; mixed Hodge structures; Iitaka's conjecture Fujino, Osamu, Notes on the weak positivity theoremsalgebraic varieties and automorphism groups, Adv. Stud. Pure Math., 75, 73-118, (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. arithmetic dynamics; primitive divisors; abc conjecture; Vojta's \(1+\epsilon\) conjecture Gratton, C.; Nguyen, K.; Tucker, T. J., ABC implies primitive prime divisors in arithmetic dynamics, \textit{Bull. Lond. Math. Soc.}, 45, 1194-1208, (2013)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Siegel's theorem; unipotent representation; torsors; monodromy; unipotent bundles G. Faltings, Mathematics around Kim's new proof of Siegel's theorem, Diophantine Goemetry, Proceedings of the research program at the Centro di Ricerca Matematica Ennio de Giorgi, U. Zannier (ed.), 390 pp., 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. del Pezzo surface; effective cone; Manin's conjecture U. Derenthal, On a constant arising in Manin's Conjecture for Del Pezzo surfaces. Math. Res. Letters 14 (2007), 481-489. Zbl1131.14042 MR2318651
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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. absolute Galois group; Shafarevich's conjecture; free profinite group; quasi-free profinite group; function field; real closed field; Laurent series field Harbater, D., On function fields with free absolute Galois groups, Journal für die Reine und Angewandte Mathematik, 632, 85-103, (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. Shimura varieties; canonical models; modular varieties; Langland's conjecture 10.1307/mmj/1030132370
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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. Clifford index; Green's conjecture; k-gonal curve; linear series C. Bopp and M. Hoff, RelativeCanonicalResolution.m2--construction of relative canonical resolutions and Eagon-Northcott type compexes, a \({\mathtt{Macaulay2}}\) package. Available at http://www.math.uni-sb.de/ag-schreyer/index.php/people/researchers/75-christian-bopp, 2015.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. birational automorphism; algebraic threefold; birational rigidity; Iskovskikh's conjecture; rationality for pencils of Del Pezzo surfaces; maximal singularities Пухликов, А. В., Бирациональные автоморфизмы трехмерных алгебраических многообразий с пучком поверхностей дель пеццо, Изв. РАН. Сер. матем., 62, 1, 123-164, (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. Mordell-Weil group; Picard variety; Function field; Tate conjecture; L-function; Birch--Swinnerton-Dyer conjecture Hindry M., Pacheco A., Wazir R.: Fibrations et conjecture de Tate. J. Number Theory 112, 345--368 (2005)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. arithmetic discriminant; Vojta's inequality; height; morphisms of curves
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Odoni'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. problems of effectivity; Linnik theorem; Mordell conjecture; density theorem for representations of relative Weil groups; Hecke density theorem; Shafarevich-Tate conjectures; generation of Galois groups by Frobenius elements; distribution of Frobenius conjugacy classes; uniform distribution of Grössencharakters; Chebotarev density theorem; automorphic representations of GL(n); strong multiplicity one theorem; compatible systems of \(\ell\)-adic representations; ramification
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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 groups of curves; positive characteristic; quotients of the fundamental group; Abhyankar's conjecture; formal/rigid-analytic patching -, Fundamental groups of curves in characteristic \(p\), in Proceedings of the International Congress of Mathematicians, 1, 2 (Zürich, 1994), Birkhäuser, 1995, pp. 656-666.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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; upper bound for the Arakelov degree; Szpiro conjecture; Arakelov metric; bounding the height of a semi-stable elliptic curve; Weierstrass sections Frey, Gerhard; Kani, Ernst, Curves of genus \(2\) covering elliptic curves and an arithmetical application.Arithmetic algebraic geometry, Texel, 1989, Progr. Math. 89, 153-176, (1991), Birkhäuser Boston, Boston, MA
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Van de Van-Bogomolov-Miyaoka-Yau inequality; torsion; Tate height; number of integral points; Mordell conjecture [19] Parshin (A.~N.).-- On the application of ramified coverings in the theory of diophantine equations. Math. USSR Sbornik 60, p.~249-264 (1990). &MR~9 | &Zbl~0702.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Namba's conjecture; hypergeometric series over finite fields; elliptic curves; trace of the Frobenius map Koike, M., Orthogonal matrices obtained from hypergeometric series over finite fields and elliptic curves over finite fields, Hiroshima Math. J., 25, 1, 43-52, (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. rational surface singularity; Kollár's conjecture; symbolic algebra; modifications
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. canonically polarized manifold; varieties of general type; Shafarevich's conjecture; Viehweg's conjecture; special varieties; geometric orbifold K. Jabbusch & S. Kebekus, ``Families over special base manifolds and a conjecture of Campana'', Math. Z.269 (2011) no. 3-4, p. 847-878
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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; values of L-functions; Grothendieck's purity conjecture; Riemann-Roch problem; Atiyah-Bott fixed point formula; Tate conjecture; construction of a motivic cohomology theory; algebraic K- theory; topological K-theory; algebraic objects; stable homotopy objects Thomason, R. W.: Survey of algebraic versus étale topologicalK-theory,Algebraic K-Theory and Algebraic Number Theory, Contemporary Mathematics 83, Amer. Math. Soc., Providence (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. elliptic surface; canonical height; elliptic curve; Szpiro conjecture; Lang conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. threefolds with canonical singularities; Fujita's freeness conjecture; Gorenstein terminal singularities; quotient singularities Kakimi, N.: On the multiplicity of terminal singularities on threefolds
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Calabi-Yau threefold; rigid; Serre's conjecture; modularity; Serre reciprocity Gouvêa, Fernando Q. and Yui, Noriko, Rigid {C}alabi--{Y}au threefolds over {\(\mathbb Q\)} are modular, Expositiones Mathematicae, 29, 1, 142-149, (2011)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow groups; motives; multiplicative Chow-Künneth decomposition; Beauville's ``(weak) splitting property''; verra fourfolds; hyperkähler varieties
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. vector bundle; stability; syzygy bundles; Butler's conjecture; Mistretta-Stoppino 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. parallel algebraic complexity; NC complexity; real algebraic numbers; Thom's lemma; multivariate Sturm theory Cucker, F.; Lanneau, H.; Mishra, B.; Pedersen, P.; Roy, M. F.: NC algorithms for real algebraic numbers, applicable algebra in engineering. Comm. comput. 3, 79-98 (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. complex multiplication; Hodge conjecture on abelian varieties; Hodge cycle; Weil cycles Y. André, Une remarque à propos des cycles de Hodge de type CM , Seminaire de Théorie des Nombres, Paris, 1989-1990, Progr. Math., vol. 102, Birkhäuser, Boston, 1992, pp. 1-7.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Novikov's conjecture; Jacobians; Kadomtsev-Petviashvili equation; principally polarized abelian varieties; Jacobian
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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 over function fields; discrete embedding of curve; Néron-Tate height pairing; admissible pairing; Green function; semistable arithmetic surface A. Moriwaki, Bogomolov conjecture over function fields for stable curves with only irreducible fibers, Compos. Math. 105 (1997), 125-140.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Abhyankar's lemma; perfectoid spaces; Riemann extension theorem; almost purity; almost algebra
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Serre conjecture; Hilbert's Nullstellensatz; Quillen-Suslin theorem Fitchas, N.; Galligo, A., Nullstellensatz effectif et conjecture de Serre (théorème de Quillen-Suslin) pour le calcul formel, Math. nachr., 149, 231-253, (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. zeta functions; distribution of zeros; \(L\)-functions; finite fields; automorphic \(L\)-functions; GUE measure; Montgomery-Odlyzko law; normalized spacings; Wigner measure; Kolmogoroff-Smirnov discrepancy function; generalized Sato-Tate conjecture; low-lying zeros; \(L\)-functions of elliptic curves; spacings of eigenvalues; Haar measure; Fredholm determinants; Deligne's equidistribution theorem; monodromy; Kloosterman sums N.M. Katz and P. Sarnak. \textit{Random matrices, Frobenius eigenvalues, and monodromy, vol. 45 of American Mathematical Society Colloquium Publications}. American Mathematical Society, Providence, RI (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. small points; abelian variety; essential minimum; Bogolomov'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. higher degree diophantine equations; elliptic curves; modular representations; Taniyama-Weil conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. height function; thin set; finite cover of degree at least three; multiplicative height N. Broberg, Rational points on finite covers of \(\mathbb P^1\) and \(\mathbb P^2\) , J. Number Theor. 101 (2003), 195-207.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. number of mappings of algebraic curves; theorem of De Franchis; Mordell's conjecture over functions fields
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. transcendental number theory; abelian varieties; surfaces; rational points; diophantine geometry; Mordell's conjecture B. Mazur, \textit{The topology of rational points}, Exp. Math. \textbf{1}(1992), no. 1, 35-45.
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