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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. special value of \(L\)-functions; Galois group; mixed elliptic motives; elliptic polylogarithm; Beilinson's conjecture A.\ B. Goncharov, Mixed elliptic motives, Galois representations in arithmetic algebraic geometry, London Math. Soc. Lecture Note Ser. 254, Cambridge University Press, Cambridge (1998), 147-221.
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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 points on algebraic curves; rational point; Jacobian; linear form of logarithms; Mordell-Weil group; height Hirata-Kohno N. , Une relation entre les points entiers sur une courbe algébrique et les points rationnels de la jacobienne , in: Advances in Number Theory , Kingston, ON, 1991 , Oxford University Press , New York , 1993 , pp. 421 - 433 . MR 1368438 | Zbl 0805.14009
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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; elliptic curves; regulators; Mordell-Weil
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. family of curves; Arakelov inequality; Higgs bundle; Beauville'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. Bibliography; geometric invariant theory; rationality of the field of invariants; constructive invariant theory; Hilbert's 14th problem; Poincaré series; categorical quotients; Russian conjecture Popov, V. L.; Vinberg, È. B., Invariant theory, (Algebraic Geometry. IV, Encyclopaedia of Mathematical Sciences, vol. 55, (1994), Springer-Verlag Berlin), (1989), Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform. Moscow, edited by A.N. Parshin and I.R. Shafarevich, vi+284 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. adjoint linear system; Fujita's conjecture; positive characteristic
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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. Jacobian fibration; elliptic fibration; Mordell-Weil group; height pairing; K3 surface
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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. theta height; curves; abelian varieties; Jacobians; Shafarevich conjecture; bounds for height; effective Mordell Rémond, G., Hauteurs thêta et construction de Kodaira, J. Number Theory, 78, 287-311, (1999)
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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 conjecture; Rational points; Seminar; Bonn/Germany; Wuppertal/Germany; proof of Tate conjecture; proof of Shafarevich conjecture; proof of the Mordell conjecture; logarithmic singularities; compactification of the moduli space of abelian varieties; modular height of an abelian variety; p-divisible groups; intersection theory on arithmetic surfaces; Riemann- Roch theorem; Hodge index theorem; rational points G. FALTINGS - G. WÜSTHOLZ, Rational points, Aspects of Math., Vieweg, 1986. Zbl0636.14019 MR863887
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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 dynamical system; Weil height
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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 upper-half space; thetanullwerte; Riemann's theta formula; theta functions Salvati Manni, R., \textit{on the dimension of the vector space} C[\(\theta\)\_{}\{m\}]\_{}\{4\}, Nagoya Mathematical Journal, 98, 99-107, (1985)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Fano varieties; quantum cohomology; mirror symmetry; Dubrovin's conjecture; gamma class; apery constant; derived category of coherent sheaves; exceptional collection; Landau-Ginzburg model
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. curves of genus \(g\); Green's conjecture; Koszul 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 curve; Gorenstein curve; Max Noether's theorem; Clifford index; Koszul cohomology; Green's conjecture. Contiero, A.; Feital, L.; Martins, R. V., MAX Noether's theorem for integral 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. Taniyama's conjecture; Fermat's last theorem
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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. Mumford's fake plane; surfaces of general type; minimal elliptic surface; Bloch conjecture Barlow R.N.: Zero-Cycles on Mumford's Surface, vol. 126, pp. 505--510. Math. Proc. Camb. Phil. Soc, Cambridge (1999)
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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; Manin's conjecture; spherical varieties; Fano threefolds
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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. theta function; multiple theta function; contiguous relation; Jacobi's triple product identity; addition formula; Stanley's lemma
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. \(L\)-function; \(F\)-crystal; Katz's conjecture; Dwork trace formula Wan, Daqing, Meromorphic continuation of \(L\)-functions of \(p\)-adic representations, Ann. of Math. (2), 143, 3, 469-498, (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. degenerations of Kummer surfaces; abelian surface; Nieto's quintic threefold; toroidal compactification of the Siegel modular threefold
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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's reciprocity law; special values of arithmetic Siegel modular functions; Siegel space W.L. Baily, Jr., On the Proof of the Reciprocity Law for Arithmetic Siegel Modular Functions, Proc. Indian Acad. Sci. Math. Sci.97 (1987), no. 1-3 (1988), 21--30.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Vojta's conjectures; function fields; fibered threefolds; heights; \(S\)-units
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Frobenius splittings; residual normal crossing; Wahl's conjecture; characteristic \(p\); homogeneous space; Wahl conjecture; surjectivity of the Gaussian map V. Lakshmibai, V. B. Mehta, A. J. Parameswaran, Frobenius splittings and blow-ups, J. Algebra 208 (1998), no. 1, 10128.
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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. Bounded Height Conjecture; Torsion Finiteness Conjecture E. Bombieri, D. Masser et U. Zannier, Intersecting a plane with algebraic subgroups of multiplicative groups. Ann. Scuola Norm. Sup. Pisa Série V 7 (2008) 51-80. Zbl1150.11022 MR2413672
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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 cohomology; pseudoconvex; commutator; Poincaré-Dolbeault lemma; Courant's minimal principle; compact Kähler space; Hodge spectral sequence Ohsawa, T., Hodge spectral sequence on compact Kähler spaces, Publ. Res. Inst. Math. Sci., 23, 265-274, (1987)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. reducible algebraic curves; Clifford index; Green'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. Cox rings; algebraic varieties; homogeneous spaces; graded algebras and rings; line bundles; toric varieties; geometric invariant theory; actions of groups; algebraic surfaces; Mori Dream Spaces; Zariski decompositions; Manin's conjecture; Hasse principle; Brauer-Manin obstructions; del Pezzo surfaces; \(K3\) surfaces; Enriques surfaces; GKZ decompositions; GALE transformations; flag varieties; combinatorial methods in algebraic geometry Arzhantsev, Ivan; Derenthal, Ulrich; Hausen, Jürgen; Laface, Antonio, Cox rings, Cambridge Studies in Advanced Mathematics 144, viii+530 pp., (2015), Cambridge University Press, Cambridge
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. algebraic cycles; Chow groups; motives; \(K3\) surfaces; cubic hypersurfaces; Fano varieties of lines; Franchetta conjecture; hyper-Kähler varieties; Beauville ``splitting property'' conjecture; multiplicative Chow-Künneth decomposition
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Voevodsky's nilpotence conjecture; noncommutative motives; noncommutative algebraic geometry; derived category; cubic fourfolds; Gushel-Mukai fourfolds; noncommutative \(K3\) surfaces
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Abhyankar's conjecture; covering of affine line; Sylow \(p\)-group; Galois group of covering
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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. multiplier ideal; test ideal; \({\mathfrak a}^t\)-tight closure; uniform bound; Fujita's freeness conjecture Hara, N., A characteristic \(p\) analog of multiplier ideals and applications, Commun. Algebra, 33, 3375-3388, (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. algebraic cycles; Chow groups; motives; finite-dimensional motives; cubics; Bloch conjecture; smash-nilpotence conjecture; Murre's conjectures Laterveer, R.: Algebraic cycles on Fano varieties of some cubics, submitted
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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. Beilinson's conjecture; tame symbol; regulator Liu, Hang; de Jeu, Rob, On \(K_2\) of certain families of curves, Int. Math. Res. Not. IMRN, 21, 10929-10958, (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. Gieseker's lemma; linear system
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. commutative cancellative torsion-free monoid; monoid ring; \(K\)-homotopy invariance; multiplicative action; nilpotence conjecture; toric variety; local-global patching; Mayer-Vietoris sequence for singular varieties; excision; pyramidal descent; big Witt vectors; nil-\(K\)-theory Joseph Gubeladze, Higher \?-theory of toric varieties, \?-Theory 28 (2003), no. 4, 285 -- 327.
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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. special cycles; generating functions; Jacobi forms; Kudla's modularity conjecture; theta series; unitary Shimura 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. algebraic cycles;Chow groups; motives; Voisin's conjecture; Calabi-Yau varieties of dimension at most 5
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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; holonomic \(D\)-module; Simpson's conjecture of moduli for semi-stable \(\Lambda\)-modules; conormal bundles; Lagrangian subset; Riemann-Hilbert correspondence Nitsure, N.: Moduli of regular holonomic D-modules with normal crossing singularities. Duke math. J. 99, 1-39 (1999)
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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. metrized vector bundles; compactified representations; height of the flag varieties; heights on the projective space; height on the moduli space of vector bundles over an algebraic curve Gasbarri, C., Heights and geometric invariant theory, Forum Mathematicum, 12, 135-153, (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. modular form; \(p\)-adic \(L\)-function; \(p\)-adic height; Heegner cycle; Euler systems; conjecture of Beilinson and Bloch J. Nekovář, On the \textit{p}-adic height of Heegner cycles, Math. Ann. 302 (1995), no. 4, 609-686.
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. equidistribution theorem; Neron-Tate height; generalized Bogomelov conjecture Zhang, S., \textit{equidistribution of small points on abelian varieties}, Ann. of Math. (2), 147, 159-165, (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. irreducible symplectic varieties; hyperkähler manifolds; base locus; Fujita'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. Vojta's conjecture; Griffiths' conjecture; rational surfaces; subspace theorem; \(abc\) conjecture; Farey sequences
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. cubic hypersurfaces; Weil's conjectures; finite fields; Fano varieties; intermediate Jacobian; irrational 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. narrow Mordell-Weil lattice; group of rational points on an elliptic curve; Weyl groups as Galois groups; Mordell-Weil lattices; sphere packing; algebraic equations; inverse Galois problem; Kodaira-Néron model; height pairing; Néron-Severi group; rational elliptic surface
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Diophantine sets; recursively enumerable sets; Arithmetic of algebraic varieties; Diophantine problems; Tate conjecture; isogenies of abelian varieties; Zeta-functions; L-functions; automorphic forms; automorphic representations; arithmetic scheme; Weil conjecture; modular forms; Galois representations
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Reider theorem; smooth toric surface; adjoint line bundle; lattice polygon; Pick theorem; Fujita'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. families of varieties; log canonical varieties; Shafarevich'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. height of cycles; complete scheme; line bundles; height machine; Néron- Tate heights Gubler, Walter, Höhentheorie, Math. Ann., 298, 3, 427-455, (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. Lang's conjecture; function fields; hypersurfaces; algebraic Morse inequalities; jet spaces Christophe Mourougane, ''Families of hypersurfaces of large degree'', J. Eur. Math. Soc. (JEMS)14 (2012) no. 3, p. 911-936 |
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Lang-Trotter conjecture; good reduction; \(\ell \)-adic representation; elliptic curve; Chebotarev's density
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic 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 varities; Coleman's conjecture; uniform isogeny 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. \(T\)-varieties of complexity one; basepoint free divisors; Fujita's Freeness Conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. proof of Mordell conjecture; proof of Tate conjecture; proof of; Shafarevich conjecture; height of Abelian variety; rational points; on elliptic curves Deligne, P., Preuve des conjectures de Tate et de shafarevitch (d'après G. faltings), Asterisque, 121-122, 25-41, (1985)
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Sullivan's rational homotopy; non-nilpotent; Toën's schematic homotopy types; Baues-Lemaire conjecture; schematic homotopy groups Isaksen, Daniel C.: Strict model structures for pro-categories. In: Categorical decomposition techniques in algebraic topology (Isle of Skye, 2001), volume 215 of Progr. Math., pages 179-198. Birkhäuser, Basel. arXiv:math/0108189 [math.AT] (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. conjugacy classes of the Monster sporadic group; Picard groups; elliptically fibered Calabi-Yau threefolds; F-theory; McKay'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. families of canonically polarized manifolds; varieties of general type; Shafarevich's conjecture; Viehweg's conjecture; log Fano varieties Lohmann, D.: Families of canonically polarized manifolds over log Fano varieties (2011). arXiv:1107.4545v1
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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. extensions of function field; generic Galois extension; Kummer theory; Leopoldt's conjecture; cyclotomic fields; geometric class field theory C. Greither, Cyclic Galois extensions of commutative rings. Lecture Notes in Mathematics, vol. 1534. Springer, Berlin-Heidelberg-New York, 1992. Zbl0788.13003 MR1222646
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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 deformations; cusp forms; functional equation of \(L\)-series; order of vanishing of the \(L\)-function; elliptic curve; Mordell-Weil group; Selmer group; Birch and Swinnerton-Dyer conjecture Greenberg, R.: Elliptic curves and p-adic deformations. In: Kisilevsky, H., Ram Murty, M. (eds.) Elliptic Curves and Related Topics. CRM Proceedings and Lecture Notes, vol. 4, pp. 101--110. American Mathematical Society, Providence, RI (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. factorial ring of automorphic forms; Satake compactification; Picard group; theta constant; Schottky invariant; Mumford's conjecture; second Betti number; moduli space of non-hyperelliptic curves S. Tsuyumine: Factorial property of a ring of automorphic forms. Trans. Amer. Math. Soc. (to appear). JSTOR:
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Hartshorne's conjecture; complete intersection; special Cremona transformations Crauder, B., Katz, S.: Cremona transformations and Hartshorne's conjecture. Am. J. Math. 113(2), 269--285 (1991)
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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. twisted arithmetic Siegel-Weil formula; Kronecker limit formula; arithmetic intersection
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. curves; syzygies; Green'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. Poincaré's lemma; Koszul complex; Eagon-Northcott complex
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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; intrinsic quadrics; global field; positive characteristic D. Bourqui, La conjecture de Manin géométrique pour une famille de quadriques intrinsèques , Manuscripta Math. 135 (2011), no. 4, 1-41.
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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. non-commutative schemes; Morita theorem; quasicoherent sheaves; Azumaya algebras; Căldăraru's conjecture; non-commutative 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. modularity; Langlands-Tunnell theorem; Serre's conjecture; 5-division points; elliptic curve; 2-division points; Abelian surface Shepherd-Barron, NI; Taylor, R, Mod \(2\) et mod \(5\) icosahedral representations, J. Am. Math. Soc, 10, 283-298, (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. Graded rings; Filtrations; Commutative rings; Proceedings; Symposium; Kyoto/Japan; filtrations; Buchsbaum modules; Sharp's conjecture; derivations; Cohen- Macaulay; graded rings
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heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. canonical measures; Chebyshev polynomials; equidistribution; height; integral points; preperiodic points doi:10.1016/j.jnt.2010.10.003
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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. Schubert classes; symplectic Grassmannians; torus equivariant cohomology; Giambelli type formula; Wilson's conjecture; double Schubert polynomials Ikeda, T.; Matsumura, T., \textit{Pfaffian sum formula for the symplectic Grassmannians}, Math. Z., 280, 269-306, (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. Weil pairing; Tate pairing; pairing computation; abelian varieties; Miller's algorithm DOI: 10.1016/j.jsc.2014.08.001
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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. covariants; invariant theory; no-name lemma; Speiser's lemma Domokos, M., Covariants and the no-name lemma, J. Lie Theory, 18, 839-849, (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. Archimedean height pairing; Green's current; algebraic cycle; Kähler manifold
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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. Chowla's conjecture; \(L\)-functions; zeta functions of curves; Carlitz extensions; cyclotomic function fields; abelian varieties over finite 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. stability; Clifford index; Green's conjecture Paranjape K and Ramanan S, \textit{On the canonical ring of a curve, in: Algebraic geometry and commutative algebra, vol. II} (1988) (Tokyo: Kinokuniya) pp. 503-516
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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. topological algebras; geometric topological algebras; Gel'fand presheaf; topological algebra scheme; locally affine; local information; Yoneda functor; Yoneda's lemma; functor of points, spectrum functor; Šilov's problem; dynamical algebra; dynamical relativistic localization; Einstein topological algebra space; extension of scalars functor; abstract/modern differential geometry; ADG; Heisenberg's incompatibility; principle of locality Mallios, A.: On algebra spaces. Contemp. Math. 427, 263--283 (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. curves; genus; morphism; Faltings theorem; Mordell conjecture; algebraic curve of genus greater than one; method of Demyanenko-Manin; rational points; height; Birch and Swinnerton-Dyer conjecture Kulesz, L.; Application de la méthode de Dem'janenko-Manin à certaines familles de courbes de genre 2 et 3; J. Number Theory: 1999; Volume 76 ,130-146.
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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. Néron-Tate canonical height; Bogomolov conjecture; Belyĭ map
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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; sums of squares; class number problem; imaginary quadratic fields; Gauss' conjecture; modular elliptic curve; Hasse-Weil L-function; class-number-one problem \BibAuthorsD. Goldfeld, Gauss' class number problem for imaginary quadratic fields, Bull. Amer. Math. Soc. 13 (1) (1985), 23--37.
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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. Dwork's conjecture; \(p\)-adic meromorphic continuation; unit root \(L\)-function; algebraic varieties; finite field of characteristic \(p\); arithmetic of modular forms; Gouvêa-Mazur conjecture Wan, D, A quick introduction to dwork's conjecture, Contem Math., 245, 147-163, (1999)
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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; cubic surface; asymptotic; singular; quadratic congruence; average; large sieve; real characters Baier, S.; Derenthal, U.: Quadratic congruences on average and rational points on cubic surfaces, (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. Igusa compactification; Siegel modular variety; moduli space of genus 2 curves; Weierstrass points; zeta function; characteristic p; Weil conjectures Ronnie Lee and Steven H. Weintraub, Cohomology of a Siegel modular variety of degree 2, Group actions on manifolds (Boulder, Colo., 1983) Contemp. Math., vol. 36, Amer. Math. Soc., Providence, RI, 1985, pp. 433 -- 488.
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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. Iwasawa \(\mu\)-invariant; elliptic curves over global fields; Greenberg's conjecture; Selmer group Mak Trifković, On the vanishing of \(\mu \)-invariants of elliptic curves over \(\mathbb Q\), Canad. J. Math. 57 (2005), no. 4, 812-843.
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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. reductive group schemes; principal G-bundles; Grothendieck-Serre'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. invariant subrings; affine local domain; high-order derivations; regularity; Nakai'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. Abelian variety of GL\(_2\)-type; Ribet's conjecture Pyle, E. E., Modular Curves and Abelian Varieties, 224, Abelian varieties over \(\mathbb Q\) with large endomorphism algebras and their simple components over \(\overline{\mathbb Q}\), 189-239, (2004), Birkhäuser: Birkhäuser, Basel
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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. Berkovich analytic spaces; formal geometry; Chambert-Loir's measures; tropical varieties; equidistribution Gubler, W., \textit{non-Archimedean canonical measures on abelian varieties}, Compositio Math., 146, 683-730, (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. global fields; algebraic curves and surfaces; abelian varieties; zeta and \(L\)-function; Brauer-Siegel theorem; Birch and Swinnerton-Dyer conjecture; Bloch-Kato conjecture
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. étale cover of curve; characteristic \(p\); Galois groups; Abhyankar'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. representation theory; reductive algebraic groups; simple modules; highest weights; character formulas; Weyl's character formula; affine group schemes; injective modules; injective resolutions; derived functors; Hochschild cohomology groups; hyperalgebra; split reductive group schemes; Steinberg's tensor product theorem; irreducible representations; Kempf's vanishing theorem; Borel-Bott-Weil theorem; characters; linkage principle; dominant weights; filtrations; Steinberg modules; cohomology rings; rings of regular functions; Schubert schemes; line bundles; Schur algebras; quantum groups; Kazhdan-Lusztig polynomials J. C. Jantzen, \textit{Representations of Algebraic Groups. Second edition}, Amer. Math. Soc., Providence (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. Hasse-Weil \(L\)-function; Birch-Swinnerton-Dyer conjecture; elliptic curve; complex multiplication M. Ram Murty and V. Kumar Murty, Base change and the Birch-Swinnerton-Dyer conjecture, A tribute to Emil Grosswald: number theory and related analysis, Contemp. Math., vol. 143, Amer. Math. Soc., Providence, RI, 1993, pp. 481 -- 494.
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. canonical heights; divisibility sequences; hyperelliptic curves; division polynomial; hyperelliptic sigma function; local height
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Hilbert modular surface; Hirzebruch-Zagier divisor; arithmetic intersection; Colmez conjecture; Igusa invariants; Faltings' height Yang, T. H., \textit{arithmetic intersection on a Hilbert modular surface and the faltings height}, Asian J. Math., 17, 335-381, (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. Hecke operators on Hilbert varieties; estimates of eigenvalues; Hecke ring; Hilbert modular variety; \(\ell\)-adic cohomology; local zeta function; toroidal compactifications; Weil conjecture K. Hatada: On the local zeta functions of compactified Hilbert modular schemes and action of the Hecke rings. Sci. Rep. Fac. Ed. Gifu Univ. Natur. Sci., 18, no. 2, 1-34 (1994).
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. monomial curve; symmetric numerical semigroup; gluing; Gorenstein; Hilbert function of a local ring; Rossi's conjecture Arslan, F.; Sipahi, N.; Şahin, N., Monomial curve families supporting Rossi's conjecture, J. symbolic comput., 55, 10-18, (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. Mordell-Lang-type conjecture; Strassman's theorem
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. survey; Birch-Swinnerton-Dyer conjecture; Herbrand-Ribet theorem; Fermat's Last Theorem
| 0 |
heights; Mahler measures; multiplicative Weil height; Siegel's lemma; Lehmer's conjecture; Dobrowolski's result Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. elliptic curve; Weil height; canonical height; Mordell-Weil group Silverman, J.H.; The difference between the Weil height and the canonical height on elliptic curves; Math. Comp.: 1990; Volume 55 ,723-743.
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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. explicit formulas; Fubini-study height of quadrics; Igusa's zeta functions Dan, N.: La hauteur des quadriques. C. R. Acad. sci. Paris sér. I math. 324, 1323-1326 (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. arithmetic geometry; Lang's conjecture; fibered power conjecture; uniformity of rational points; varieties of general type; positive characteristic Dan Abramovich and José Felipe Voloch, Lang's conjectures, fibered powers, and uniformity, New York J. Math. 2 (1996), 20 -- 34, electronic.
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