Abstract:
This article studies representations of semisimple Lie algebras arising naturally in the l-adic cohomology of algebraic varieties defined over global fields. A conjecture is formulated about the restrictions the index of the cohomology space and the Hodge numbers of a variety impose on the weights of a represention. The conjecture is proved for ordinary varieties over function fields. An analog of the conjecture is valid for the rational cohomology of varieties defined over the field of complex numbers.
Bibliography: 41 titles.
\Bibitem{Zar84}
\by Yu.~G.~Zarhin
\paper Weights of simple Lie algebras in the cohomology of algebraic varieties
\jour Math. USSR-Izv.
\yr 1985
\vol 24
\issue 2
\pages 245--281
\mathnet{http://mi.mathnet.ru/eng/im1446}
\crossref{https://doi.org/10.1070/IM1985v024n02ABEH001230}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=740792}
\zmath{https://zbmath.org/?q=an:0579.14019}
Linking options:
https://www.mathnet.ru/eng/im1446
https://doi.org/10.1070/IM1985v024n02ABEH001230
https://www.mathnet.ru/eng/im/v48/i2/p264
This publication is cited in the following 40 articles:
S. G. Tankeev, “Toric geometry and the standard conjecture for a compactification of the Néron model of Abelian variety
over 1-dimensional function field”, Izv. Math., 89:1 (2025), 140–171
S. G. Tankeev, “On the standard conjecture for a fourfold with
1-parameter fibration by Abelian varieties”, Izv. Math., 88:2 (2024), 339–368
Yuri G. Zarhin, Simons Symposia, Arithmetic and Algebraic Geometry, 2024, 389
Wojciech Gajda, Sebastian Petersen, “Local to global principles for homomorphisms of abelian schemes”, Isr. J. Math., 257:1 (2023), 281
O. V. Makarova, “On algebraic isomorphisms of cohomology of a compactification of the Néron model with multiplications from an imaginary quadratic field”, Sib. elektron. matem. izv., 19:1 (2022), 34–48
S. G. Tankeev, “On the standard conjecture for compactifications of Néron models of 4-dimensional Abelian varieties”, Izv. Math., 86:4 (2022), 797–835
S. G. Tankeev, “On the standard conjecture for projective compactifications of Néron models of 3-dimensional
Abelian varieties”, Izv. Math., 85:1 (2021), 145–175
S. G. Tankeev, “On algebraic isomorphisms of rational cohomology of a Künneman compactification of the Néron minimal model”, Sib. elektron. matem. izv., 17 (2020), 89–125
S. G. Tankeev, “On the standard conjecture for a 3-dimensional variety fibred by curves with a non-injective Kodaira–Spencer map”, Izv. Math., 84:5 (2020), 1016–1035
O. V. Makarova, “Invariant Cycles on Abelian Schemes”, J Math Sci, 250:1 (2020), 69
S. G. Tankeev, “On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci”, Izv. Math., 83:3 (2019), 613–653
Damian Rössler, Tamás Szamuely, “Cohomology and torsion cycles over the maximal cyclotomic extension”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2019:752 (2019), 211
O. V. Nikolskaya, “Ob algebraicheskikh tsiklakh na rassloennykh proizvedeniyakh neizotrivialnykh semeistv regulyarnykh poverkhnostei s geometricheskim rodom 1”, Model. i analiz inform. sistem, 23:4 (2016), 440–465
S. G. Tankeev, “On the standard conjecture and the existence of a Chow–Lefschetz decomposition for complex projective varieties”, Izv. Math., 79:1 (2015), 177–207
Orr M., “Lower Bounds For Ranks of Mumford-Tate Groups”, Bull. Soc. Math. Fr., 143:2 (2015), 229–246
O. V. Nikol'skaya, “On the geometry of a smooth model of a fibre product of families of K3 surfaces”, Sb. Math., 205:2 (2014), 269–276
S. G. Tankeev, “On the standard conjecture for complex 4-dimensional elliptic varieties and compactifications of Néron minimal models”, Izv. Math., 78:1 (2014), 169–200
O. V. Nikol'skaya, “On Algebraic Cohomology Classes on a Smooth Model of a Fiber Product of Families of K3 surfaces”, Math. Notes, 96:5 (2014), 745–752
O. V. Nikol'skaya, “On algebraic cycles on a fibre product of families of K3-surfaces”, Izv. Math., 77:1 (2013), 143–162
Citation in format AMSBIB
Contact us: