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Algebraic cycles on a simple 4P-dimensional abelian variety over a number field

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References

  1. F. A. Bogomolov, “Points of finite order on an Abelian variety”,Izv. Akad. Nauk SSSR, Ser. Mat.,44, No. 4, 782–804 (1980).

    MATH  MathSciNet  Google Scholar 

  2. M. V. Borovoi, “Schemes Shimura-DelignM ℂ(G,h) and rational cohomology class of type (p, p) of Abelian varieties”, InQuestions of Group Theory and of Homological Algebra [in Russian] YarGU, Yaroslavl (1977), pp. 3–53.

    Google Scholar 

  3. Yu. G. Zarkhin, “Abelian varieties,l-adic representations, and\(\mathbb{S}\mathbb{L}_2 \)”,Izv. Akad. Nauk SSSR, Ser. Mat.,43, No. 2, 294–308 (1979).

    MATH  MathSciNet  Google Scholar 

  4. Yu. G. Zarkhin, “Weights of simple Lie algebras in cohomology of algebraic varieties”,Izv. Akad. Nauk SSSR, Ser. Mat.,48, No. 2, 264–304 (1984).

    MATH  MathSciNet  Google Scholar 

  5. I. I. Pyatetskii-Shapiro, “Interrelations between conjectures of Tate and Hodge for Abelian varieties”,Mat. Sb.,85, No. 4, 610–620 (1971).

    MATH  MathSciNet  Google Scholar 

  6. S. G. Tankeev, “On algebraic cycles on surfaces and Abelian varieties”,Izv. Akad. Nauk SSSR, Ser. Mat.,45, No. 2, 398–434 (1981).

    MATH  MathSciNet  Google Scholar 

  7. S. G. Tankeev, “Cycles on prime Abelian varieties of prime dimension”,Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 1, 155–170 (1982).

    MathSciNet  Google Scholar 

  8. S. G. Tankeev, “Cycles on prime Abelian Varieties of prime dimension over number fields”,Izv. Akad. Nauk SSSR, Ser. Mat. 51, No. 6, 1214–1227 (1987).

    MATH  MathSciNet  Google Scholar 

  9. S. G. Tankeev, “Surfaces of K3 type over number fields and the Mumford-Tate conjecture”,Izv. Akad. Nauk SSSR, Ser. Mat.,54 No. 4, 846–861 (1990).

    Google Scholar 

  10. S. G. Tankeev, “Algebraic cycles on an Abelian variety with no complex multiplication”,Izv. Ross. Akad. Nauk, Ser. Mat. 58, No. 3, 103–126 (1994).

    MATH  MathSciNet  Google Scholar 

  11. S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”,Izv. Ross. Akad. Nauk,60, No. 2 (1996).

    Google Scholar 

  12. J. W. S. Cassels and A. Fröhlich, eds.,Algebraic Number Theory, Academic Press, London-New York (1967).

    MATH  Google Scholar 

  13. N. Bourbaki,Groupes et Algebres de Lie. Chaps. 1–8, Hermann, Paris (1968, 1971, 1972, 1975).

    Google Scholar 

  14. W. Chi, “Onl-adic representations attached to some absolutely simple Abelian variety of the type II”,J. Fac. Sci. Univ. Tokyo. Sect. 1A. Math.,37, 467–484 (1990).

    MATH  MathSciNet  Google Scholar 

  15. W. Chi, “Onl-adic representations attached to simple Abelian varieties of the type IV”,Bull. Austral. Math. Soc.,44, 71–78 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  16. W. Chi, “l-Adic and λ-adic representations associated with Abelian varieties defined over a number field”,Amer. J. Math.,114, 315–353 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  17. P. Delign “Theorie de Hodge. II”,Inst. Hautes Etudes Sci. Publ. Math.,40, 5–57 (1972).

    Google Scholar 

  18. P. Delign, “Varieties abeliennes ordinaires sur un corps fini”,Invent. Math.,8, 238–243 (1969).

    Article  MathSciNet  Google Scholar 

  19. G. Faltings, “Endlichkeitssätze für Abelsche Varitäten über Zahlkörpern”Invent. Math.,75, 381 (1984).

    Article  MathSciNet  Google Scholar 

  20. A. Grothendieck, “The Hodge general conjecture is false for trivial reasons”,Topology,8, 299–303 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  21. F. Hazama, “The generalized Hodge conjecture for stably nondegenerate Abelian variaties”,Compos. Math.,93, 129–137 (1994).

    MATH  MathSciNet  Google Scholar 

  22. W. V. D. Hodge, “The topological invariants of algebraic varieties”, In:Proc. Int. Congr., Cambridge, Mass., Vol. 1 (1950), pp. 182–192.

  23. D. Mumford,Abelian Varieties, Tata Inst. Fund. Res. Bombay, Oxford Univ. Press, London (1979).

    Google Scholar 

  24. D. Mumford, “Families of Abelian varieties. Algebraic groups and discontinuous subgroups”Proc. Symp. Pure Math.,9, 347–352 (1966).

    MATH  MathSciNet  Google Scholar 

  25. J.-P. Serre,Abelian l-Adic Representations and Elliptic Curves, Benjamin New York (1968).

    MATH  Google Scholar 

  26. J.-P. Serre, “Groupes algebriques associes aux modules de Hodge”,Asterisque,65, 155–188 (1979).

    MATH  MathSciNet  Google Scholar 

  27. G. Shimura, “On analytic families of polarized Abelian varietes and automorphic functions”,Ann. Math.,78, 149–192 (1963).

    Article  MATH  MathSciNet  Google Scholar 

  28. J. Tate, “Algebraic cycles and poles of zeta function”, In:Arithmetical Algebraic Geometry, New York (1965), pp. 93–110.

  29. J. Tate, “Classes d'isogenie des varietes abeliennes sur un corp fini (d'apres T. Honda)”Lect. Notes Math.,179, 95–110 (1971).

    Article  Google Scholar 

  30. Yu. G. Zarkhin, “Abelian varietes having a reduction of K3 type”,Duke J. Math.,65, No. 3, 511–527 (1992).

    Article  MATH  MathSciNet  Google Scholar 

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  1. S. G. Tankeev
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 35, Algebraicheskaya Geometriya-6, 1996.

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Tankeev, S.G. Algebraic cycles on a simple 4P-dimensional abelian variety over a number field. J Math Sci 90, 2287–2321 (1998). https://doi.org/10.1007/BF02433954

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