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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. Gromov-Witten potential; Kähler manifold; Givental's quantization; Witten's r-spin conjecture. Chiodo, A.; Zvonkine, D., Twisted \(r\)-spin potential and Givental's quantization, Adv. Theor. Math. Phys., 13, 5, 1335-1369, (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. integral point; Vojta's conjecture; subspace theorem P. Corvaja and U. Zannier, Integral points, divisibility between values of polynomials and entire curves on surfaces, Adv. Math. 225 (2010), no. 2, 1095-1118.
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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. Pisot's \(d\)-th root conjecture; function fields; linear recurrences; GCD estimates
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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. rank 3 simple matroids; Terao's freeness conjecture; fitting ideals; multiarrangments; Groebner bases
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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. corrected version; Weil decomposition theorem; heights; Hilbert irreducibility theorem; G-functions; arithmetic on algebraic varieties P. Debes , Quelques remarques sur un article de Bombieri concernant le Théorème de Décomposition de Weil , Amer. J. Math. 107 ( 1985 ), 39 - 44 . MR 778088 | Zbl 0563.12010
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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 on curves; uniform bounds; Chabauty's method; \(p\)-adic integration; Mordell-lang conjecture; Zilber-Pink 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. Beilinson conjectures; Birch-Swinnerton-Dyer conjecture; Shimura- Taniyama-Weil conjecture; Tate conjectures; Hasse-Weil conjecture; Hodge conjecture; Hodge cycles; Grothendieck conjectures; mixed motives Wilfred Hulsbergen, \textit{Conjectures in Arithmetic Algebraic Geometry. }Blanchard, Paris 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. algebraic number theory; arithmetical geometry; \(p\)-adic analysis; Elkik's lemma; Tougeron's lemma; Greenberg-Schappacher theorem; Newton's lemma; Hensel's lemma; smoothness; infinitesimal lifting
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Arakelov theory; Borcherds forms; Siegel-Weil formula Kudla, S. S., \textit{integrals of borcherds forms}, Compositio Math., 137, 293-349, (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. varieties of general type; vanishing theorems; volume of a divisor; restricted volume; canonical divisor; multiplier ideals; klt pairs; non-klt locus; fujita's conjecture; augmented base locus O. Debarre, Systèmes pluricanoniques sur les variétés de type général , Astérisque 311 (2008), 119--140., Seminaire Bourbaki 2006/2007, exp.no. 970.
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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; minimal model program; rational points; Fano varieties
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. generators; relations; graded ring; ideals of cusp \(forms+\) Satake compactification; special 3-folds; Siegel's modular varieties; Siegel's modular group; modular forms; Witt's operator T. Ibukiyama: On Siegel modular varieties of level \(3\) , Internat. J. Math. 2 (1991), 17-35.
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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. tachyon scattering amplitudes; divisors with complex coefficients; moduli space of complex; algebraic curves of genus g with n given points; Belavin-Knizhnik theorem; bosonic string theory; Polyakov volume form; Weil-Deligne pairings; Arakelov measures; Quillen metrics Voronov, AA, A unified approach to string scattering amplitudes, Commun. Math. Phys., 131, 179, (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. \(M\)-curves; curve with the maximal number of connected components; Harnack's bound; Gudkov's conjecture; Hilbert's sixteenth problem; Rokhlin's formula A. I. Degtyarev and V. M. Kharlamov, ''Topological Properties of Real Algebraic Varieties: Du côté de chez Rokhlin,'' Usp. Mat. Nauk 55(4), 129--212 (2000) [Russ. Math. Surv. 55, 735--814 (2000)].
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Getzler's genus one relation; Virasoro conjecture; quantum product; Gromov-Witten invariants
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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; elliptic curves with complex multiplication; L-series; Mordell-Weil group; L-function B. H. Gross, ''On the conjecture of Birch and Swinnerton-Dyer for elliptic curves with complex multiplication,'' in Number Theory Related to Fermat's Last Theorem, Koblitz, N., Ed., Mass.: Birkhäuser, 1982, pp. 219-236.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Galois theory; motives; transcendental numbers; periods; Betti cohomology; de Rham cohomology; motivic Galois groups; period torsors; Grothendieck's period conjecture; Kontsevich; Zagier; Gamma function; Rohrlich Lang conjecture; zeta values; multiple zeta values; differential Galois theory André, Yves, Galois theory, motives and transcendental numbers.Renormalization and Galois theories, IRMA Lect. Math. Theor. Phys. 15, 165-177, (2009), Eur. Math. Soc., Zürich
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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. Weil pairing; elliptic curve; Miller's algorithm
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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. simultaneous zeros; quadratic forms; cubic forms; p-adic fields; Artin'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. diophantine equations; Siegel's theorem; integral points on affine curves; function-fields of characteristic zero José Felipe Voloch, Siegel's theorem for complex function fields, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1307 -- 1308.
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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 parametrization; Weil-Taniyama conjecture; elliptic curve; modular group J. Cremona , Computing the degree of a modular parametrization , in Algorithmic number theory ( Ithaca, NY , 1994 ), 134 - 142 , Lecture Notes in Comput. Sci. 877 , Springer , Berlin , 1994 . MR 1322718 | Zbl 0840.14018
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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; canonical metrics; integer Laurent polynomials; multiplicity; Weil height MAILLOT V. - Un théorème de Bernstein-Koushnirenko arithmétique , C. R. Acad. Sci. Paris Sér. I Math. 323, ( 1996 ), p. 977-980. MR 98c:14017 | Zbl 0870.14015
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Vojta inequality; abelian variety; Faltings theorem; Lang Conjecture; Neron-Tate height Rémond, G., Inégalité de vojta en dimension supérieure, Ann. Sc. Norm. Sup. Cl. Sci. (4), 29, 101-151, (2000)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. exceptional polynomials; inverse Galois problem; Carlitz's conjecture; general exceptional covers; nonsingular projective algebraic curves; Schur covers; monodromy pair; modular curves over finite fields; fiber products; curves of high genus M. D. Fried, \textit{Global construction of general exceptional covers}, in Finite Fields: Theory, Applications, and Algorithms, Contemp. Math. 168, G. L. Mullen and P. J. Shiue, eds., AMS, Providence, RI, 1994, pp. 69--100.
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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; integral points; Lang's conjecture; Lang-Vojta's conjecture Abramovich, D, Uniformity of stably integral points on elliptic curves, Invent. Math., 127, 307-317, (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. Seshadri constants; volume of divisors; Nagata'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. Mordell-Weil rank; Jacobian varieties; Frey-Jarden conjecture; abelian points
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Fujita's conjecture; F-amplitude; very ample; generated by global sections doi:10.1353/ajm.0.0015
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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. cancellation problems; Zariski's conjecture Belov, Alexei; Yu, Jie-Tai: Cancellation problems and dimension theory, Comm. algebra 34, No. 4, 1521-1540 (2006)
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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. hyperplane arrangements; divisionally free arrangements; Terao's Conjecture; additionally free arrangements; inductively free arrangements; stair-free 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. Green functions; Arakelov divisor class group; regular arithmetic surface; capacity pairing; Néron's local height pairing; nonarchimedean places Stanley, R.P.: Cohen-Macaulay complexes. In: Higher Combinatorics (Proc. NATO Advanced Study Inst., Berlin, 1976), (1977), pp. 51-62. NATO Adv. Study Inst. Ser. C Math. Phys. Sci. \textbf{31}
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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. K3 surfaces; mirror symmetry; Kontsevitch's conjecture; Fukaya-type category; Chern character C. Bartocci, U. Bruzzo, S. Sanguinetti, Categorial mirror symmetry for K3 surfaces, Commun. Math. Phys. 206 (1999) 265--272.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. heights; Tamagawa measures; Fano variety; rational points; del Pezzo surfaces E. Peyre, Hauteurs et mesures de Tamagawa sur les variétés de Fano, Duke Math. J. 79 (1995), no. 1, 101-218.
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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. osculating space; secant variety; Terracini's Lemma; Laplace equation; Horace method Ballico, E.; Bocci, C.; Carlini, E.; Fontanari, C.: Osculating spaces to secant varieties, Rend. circ. Mat. Palermo 53, 429-436 (2004)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Mazur's conjecture; elliptic curves; algebraic fields
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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; multiplicative dependence; geometry of numbers A. Petho, On a polynomial transformation and its application to the construction of a public key cryptosystem, in: \textit{Computational Number Theory} (Debrecen, 1989), de Gruyter (Berlin, 1991), pp. 31-43.
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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. Coates-Wiles theorem; Birch Swinnerton-Dyer conjecture; Stark conjectures; elliptic curve; Hasse-Weil zeta function Stark, H.: The Coates-Wiles theorem revisited. Number theory related to Fermat's last theorem (Progress in Math., Vol. 26). Boston: Birkhäuser 1982
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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 function fields; explicit computation of \(L\)-functions; special values of \(L\)-functions and BSD conjecture; estimates of special values; analogue of the Brauer-Siegel 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. relative regulator; Hasse index; relative discriminant; height; Salem numbers; Lehmer problem Anne-Marie Bergé & Jacques Martinet, Notions relatives de régulateurs et de hauteurs, Acta Arith.54 (1989), p. 155-170
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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; automorphism groups; nonsplit Cartan subgroups; modular automorphisms; Serre's uniformity conjecture Dose, V., On the automorphisms of the nonsplit Cartan modular curves of prime level, Nagoya Math. J., 224, 1, 74-92, (2016), MR 3572750
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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. dynamical Pink-Zilber conjecture; heights
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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 Mahler's measure; \(K3\) surfaces; modular form Bertin, M.J.: Mahler's measure and \(L\)-series of \(K3\) hypersurfaces. In: Mirror Symmetry, V, vol. 38, pp. 3-18. AMS/IP Stud. Adv. Math. Amer. Math. Soc., Providence, RI (2006)
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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. asymptotic rank of an elliptic curve; Néron-Tate height of basis points of the Mordell-Weil 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. Tamagawa numbers; Minkowski-Siegel-Tamagawa formula; linear algebraic groups; Haar measures; group of adèles; Tamagawa measures V. E. Voskresenskiĭ, Algebraic Groups and their Birational Invariants, Transl. Math. Mono., (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. general overview; Fermat's last theorem; Fermat conjecture; elliptic curves
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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. uniformly locally finite triangulation; complex projective varieties with conical singularities; real cohomology group; canonical combinatorical Laplace operator; open manifolds; infinite simplicial complexes; \(L_ 2\)-cohomology; Sobolev cohomology; analytical \(L_ 2\)-cohomology of open oriented Riemannian manifolds; de Rham-Hodge isomorphism in the \(L_ 2\)- category; Hirzebruch's conjecture; intersection homology
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. automorphic forms; endoscopy; transfer conjecture; fundamental lemma; Hitchin fibration Ngô, B.C.: Endoscopy theory of automorphic forms. In: Proceedings of the International Congress of Mathematicians, vol. I, pp. 210--237. Hindustan Book Agency, New Delhi (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. semiabelian varieties; complex multiplication; Zilber-Pink conjecture; mixed Shimura varieties; heights; \(o\)-minimality; Ribet sections
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Stillman's conjecture; sheaf cohomology
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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. singular metric; optimal \(L^2\) extension theorem; strong openness of multiplier ideal sheaf; generalized Siu's lemma; weakly pseudoconvex Kähler manifold
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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 number field; function field; normal extensions; prescribed ramification; Galois groups; Abhyankar's conjecture D. Harbater, Galois groups with prescribed ramification. Contemporary Math. 174 (1994), 35-60. Zbl0815.11053 MR1299733
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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; function fields; Birch-Swinnerton-Dyer conjecture; modular elements; modular forms; special values; \(L\)-functions; Mazur and Tate's refined conjectures; integrality; functional equation Tan K.-S., Modular elements over function fields, J. Number Theory 45 (1993), no. 3, 295-311.
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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; mixed motives; motivic cohomology; period conjecture; special values of \(L\)-functions; Deligne's conjecture; Beilinson's conjectures Anthony J. Scholl, Remarks on special values of \?-functions, \?-functions and arithmetic (Durham, 1989) London Math. Soc. Lecture Note Ser., vol. 153, Cambridge Univ. Press, Cambridge, 1991, pp. 373 -- 392.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Abelian variety; canonical height; bad reduction; Lang conjecture; Silverman conjecture J. H. Silverman, ''Lower bounds for height functions,'' Duke Math. J., vol. 51, iss. 2, pp. 395-403, 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. Weil representation; Schwartz space; Siegel upper half-plane Stoyanovsky, A V, Description of smooth vectors of the Weil representation in the geometric realization, Funct. Anal. Appl., 40, 241-243, (2006)
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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. quadratic form; Witt ring; fundamental ideal; Pfister form; Witt index; higher Witt indices; generic splitting; height of a quadratic form; stable birational equivalence; Chow motif; Tate motif; Rost motif; homogeneous variety; Rost's nilpotence theorem; Steenrod operation; motivic equivalence Kahn, B., \textit{formes quadratiques et cycles algébriques [d'après rost, Voevodsky, vishik, karpenko ...], exposé bourbaki no. 941}, Astérisque, 307, 113-163, (2006)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. heights; toric varieties; rational points; Newton polyhedron; Mellin's transform; convex analysis; mulitple Dirichlet series Essouabri, D., Height zeta functions on generalized projective toric varieties, (Zeta Functions in Algebra and Geometry, Contemp. Math., vol. 566, (2012), Amer. Math. Soc. Providence, RI), 65-98
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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. Hilbert-Burch matrices; perfect height two ideals; Dubreil's inequality; degree matrix
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Fermat's curves; Jacobians; Mordell-Weil group Sall, O.: Points algébriques de petit degré sur LES courbes de Fermat. C. R. Acad. sci. Paris sér. I 330, 67-70 (2000)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. elliptic curves; heights; canonical height; height bounds J.\ E. Cremona, M. Prickett and S. Siksek, Height difference bounds for elliptic curves over number fields, J. Number Theory 116 (2006), 42-68.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. abelian variety; Jacobian; Néron-Tate height; local Néron pairing; conjecture of Birch and Swinnerton-Dyer; Cartan modular curve of level 13
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Arakelov theory; height functions; diophantine algebraic geometry; Mordell conjecture Huisman, J.: Heights on abelian varieties. Lecture notes in math. 1566, 51-61 (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. Modell-Weil group; elliptic curve; infinite descent; logarithmic height S. Siksek, Infinite descent on elliptic curves. Rocky Mountain J. Math. 25:4 (1995), 1501-1538. Zbl0852.11028 MR1371352
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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 rank; Mordell-Weil group; elliptic fibration; at most quadratic point of elliptic surface; estimates on heights Bremner, A.: On elliptic surfaces of Mordell-Weil rank 4,Nagoya Math. J. 102, 101--115 (1986)
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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; finiteness theorems; hyperbolic manifolds; rational points; integer points; finite modulo trace; loops on complex manifolds; closed points on algebraic varieties over a finite field A. N. Parshin, ``Finiteness theorems and hyperbolic manifolds'', The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck, v. III, Progr. Math., 88, Birkhaüser, Boston, MA, 1990, 163 -- 178
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Ihara-type result; Atkin-Lehner correspondences; Siegel moduli spaces; Siegel modular forms
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. essential minimum; multiplicative group; normalized height Amoroso, F.; David, S.: Densité des points à coordonnées multiplicativement indépendantes. Ramanujan J. 5, 237-246 (2001)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. \(l\)-adic cohomology; Weil conjectures; Chebotarev density theorem; Sato-Tate conjecture; prime number theorem; Frobenian sets Serre, J.-P.: Lectures on \({N}_{X} (p)\). CRC Press, Boca Raton (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. algebraic tori; lattices; multiplicative invariants; no-name 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. Manin's conjecture; number fields; rational points; singular cubic surface Frei, C., Counting rational points over number fields on a singular cubic surface, Algebra Number Theory, 7, 1451-1479, (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. textbook; partially ordered sets; Zorn's lemma; number theory; fields; rings; abelian groups; polynomials; field extension; formal power series; polynomial rings; finite fields; power series; rational function; Bernoulli numbers; Puiseux series; Laurent series; ideals; quotient rings; factorization; Noetherian rings; prime ideals; principal ideal domains; cyclic groups; homomorphism; group action; quotient group; symmetric group; semidirect product; Sylow group; modules; free modules; commutative ring; Smith normal form; elementary divisor; Jordan form; Hermitian space; projective space; bilinear form; symplectic space; quadratic form; Kähler triples; quaternions; spinors
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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; imaginary quadratic fields; universal torsors; del Pezzo surfaces Derenthal, U.; Frei, C., Counting imaginary quadratic points via universal torsors, Compos. Math., 150, 1631-1678, (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. André's conjecture; Hodge-type subvarieties of Shimura varieties; Shimura curves A. Yafaev, ''Special points on products of two Shimura curves,'' Manuscripta Math., vol. 104, iss. 2, pp. 163-171, 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. diagonal cubic surface; Diophantine equation; smallest solution; naive height; E. Peyre's Tamagawa-type number Elsenhans A.-S., Jahnel J.: On the smallest point on a diagonal cubic surface. Exp. Math. 19, 181--193 (2010)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Mordell-Lang conjecture; Skolem-Mahler-Lech theorem; rational self-maps; étale maps 4.J.P. Bell, D. Ghioca, T.J. Tucker, \(The Dynamical Mordell-Lang Conjecture\). Mathematical Surveys and Monographs, vol. 210 (American Mathematical Society, Providence, 2016)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Mordell-Weil group; multidimensional function fields; Néron-Tate height; Mordell-Weil rank; Jacobian; independence of some rational points T. Shioda, Constructing curves with high rank via symmetry, Amer. J. Math., to appear.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. X-rank; secant varieties; rank of tensor; Terracini's question; partially symmetric tensors; Comon's conjecture Buczyński, J.; Landsberg, J.M.; Ranks of tensors and a generalization of secant varieties; Linear Algebra Appl.: 2013; Volume 438 ,668-689.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. vanishing of \(L_2\); rank of an elliptic surface; Frobenius trace; Tate's conjecture M. Rosen, J.H. Silverman, On the rank of an elliptic surface. Invent. Math. 133 (1), 43--67 (1998)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. o-minimality; strongly minimal groups; Zilber'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. annihilator; attached primes; cohomological dimension; equidimensional ring; Lynch's conjecture; local cohomology; positive characteristic
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow groups; motives; Bloch -- Beilinson filtration; hyperkähler varieties; Fano variety of lines on cubic fourfold; Voisin'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. Drinfeld modules; Erdős-Pomerance'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. Silverman's conjecture; elliptic curve; quadratic twist; rank; parity conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Kähler packings; multipoint Seshadri constant; Nagata'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. degree of modular parametrization; congruence numbers; conjecture of Taniyama and Weil; elliptic curve; Petersson norm D.~\textsc{Zagier}, Modular parametrizations of elliptic curves, Canad. Math. Bull. \textbf{28 }(1985), 372-384.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Nakai's conjecture; \(D\)-simplicity; ring of differential operators; curves; Stanley-Reisner rings William N. Traves, Nakai's conjecture for varieties smoothed by normalization, Proc. Amer. Math. Soc. 127 (1999), no. 8, 2245 -- 2248.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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; complex multiplication; p-adic L- function of an elliptic curve; Hasse-Weil L-function E. Goldstein, Minimal Lagrangian tori in Kahler-Einstein manifolds ,
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. hyperplane arrangements; Terao's conjecture; inductively free arrangements; reflection arrangements; restricted arrangements; divisionally free arrangements Röhrle, Gerhard: Divisionally free restrictions of reflection arrangements. (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. Lawson homology; motivic cohomology; semi-topological \(K\)-theory; Bloch-Kato conjecture; Suslin'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. algebraic cycles; Chow groups; motives; Voisin'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. zero estimates; arithmetic of abelian varieties; abelian integrals; Baker's method; Siegel's theorem; effective estimate for isogenies; 1- motives; isogenies between elliptic curves; Philippon's fundamental multiplicity estimate D. Bertrand, Transcendental methods in arithmetic geometry , Analytic number theory (Tokyo, 1988), Lecture Notes in Math., vol. 1434, Springer, Berlin, 1990, pp. 31-44.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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 manifold; Kähler metric; holomorphic sectional curvature; positive canonical bundle; Kobayashi's conjecture; Yau's conjecture; Calabi's conjecture Wu, D.-M.; Yau, S.-T., Negative holomorphic curvature and positive canonical bundle, Invent. Math., 204, 595-604, (2016)
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. flag varieties; Wahl's conjecture; Frobenius splitting; Gaussian; minuscule [5] J. Brown &aV. Lakshmibai, &Wahl's conjecture for a minuscule \(G / P\)&#xProc. Indian Acad. Sci. Math. Sci.119 (2009) no. 5, p.~571Article | &MR~25 | &Zbl~1192.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. \(K3\) surfaces; canonical curves; \(K3\) carpets; canonical ribbons; Green's conjecture in positive characteristic
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. differential Chow form; differential Chow variety; differential resultant; dimension conjecture; intersection theory; differential algebraic cycle; differential Stickelberger's theorem; generic differential polynomial Gao, X. S.; Li, W.; Yuan, C. M., Intersection theory in differential algebraic geometry: generic intersections and the differential Chow form, Trans. Am. Math. Soc., 365, 9, 4575-4632, (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. Arakelov-Zhang pairing; Berkovich space; Weil height
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. non-archimedean valued fields; analytic functions; \(p\)-adic cohomology; Weil conjectures; \(p\)-adic analytic varieties; action of Frobenius; rigid cohomology; \(p\)-adic analytic functions; Morita's \(p\)-adic gamma 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. arithmetic Gan-Gross-Prasad conjecture; arithmetic fundamental lemma; Rapoport-Zink spaces; special cycles Rapoport, M.; Terstiege, U.; Zhang, W., \textit{on the arithmetic fundamental lemma in the minuscule case}, Compos. Math., 149, 1631-1666, (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. modular representation theory; Lusztig's conjecture; Andersen-Jantzen-Soergel category Fiebig, P., Lanini, M.: Periodic structures on affine moment graphs II: multiplicities and modular representations (\textbf{in preparation})
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow groups; motives; Bloch conjecture; surfaces of general type; Voisin's ``spread'' method
| 0 |
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