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Lefschetz Decompositions for Quotient Varieties

Published online by Cambridge University Press:  28 May 2008

Reza Akhtar  and
Roy Joshua
Reza Akhtar
Affiliation:
Department of Mathematics, Miami University, Oxford, Ohio, 45056, USA, reza@calico.mth.muohio.edu.
Roy Joshua
Affiliation:
Department of Mathematics, Ohio State University, Columbus, Ohio, 43210, USA, joshua@math.ohio-state.edu.
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Abstract

In an earlier paper, the authors constructed an explicit Chow-Künneth decomposition for the quotient of an abelian variety by the action of a finite group. In the present paper, the authors extend the techniques used there to obtain an explicit Lefschetz decomposition for such quotient varieties.

Keywords

Lefschetz decompositionKunneth decomposition
Type
Research Article
Information
Journal of K-Theory , Volume 3 , Issue 3 , June 2009 , pp. 547 - 560
Copyright
Copyright © ISOPP 2009

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References

1.Akhtar, R. and Joshua, R., Kunneth decomposition for quotient varieties, Indag. Math. 17, no. 3 (2006), 319–344CrossRefGoogle Scholar
2.André, Y., Kahn, B. and O'Sullivan, P., Nilpotence, radicaux et structures monoïdales, Rend. Sem. Mat. Univ. Padova 108 (2002), 107–291Google Scholar
3.Arapura, D., Motivation for Hodge cycles, Preprint (to appear in Advances in Math), (2006)CrossRefGoogle Scholar
4.Beauville, A., Quelques remarques sur la transformation de Fourier dans l'anneau de Chow d'une variété abélienne. Lect. Notes. in Math. 1016 (1983), 238–260CrossRefGoogle Scholar
5.Deligne, P., La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137–252CrossRefGoogle Scholar
6.Deninger, C. and Murre, J., Motivic decomposition of Abelian schemes and the Fourier transform. J. reine und angew. Math. 422 (1991), 201–219Google Scholar
7.Guletskii, V. and Pedrini, C., Finite dimensional motives and the conjectures of Beilinson and Murre, K-Theory 30, no. 3 (2003), 243–263CrossRefGoogle Scholar
8.Hartshorne, R., Algebraic Geometry, Springer-Verlag, 1977CrossRefGoogle Scholar
9.Hilton, P. J. and Stammbach, U., Homological Algebra, GTM, Springer, 1972Google Scholar
10.Igusa, J-I., On some problems in abstract algebraic geometry. Proc. Acad. Nat. Sci. USA 41 (1955), 964–967CrossRefGoogle ScholarPubMed
11.Kahn, B., Murre, J. and Pedrini, C., On the transcendental part of the motive of a surface, preprint, (2005)Google Scholar
12.Kleiman, S., “The Standard Conjectures”, in Motives, Proc. Symp. Pure Math. 55 part 1, AMS (1994), 3–20Google Scholar
13.Kimura, S-I., Chow groups can be finite dimensional, in some sense, Math. Annalen 331 (2005), 173–201CrossRefGoogle Scholar
14.Künnemann, K., A Lefschetz decomposition for Chow motives of Abelian schemes, Invent. Math. 113 (1993), 85–102CrossRefGoogle Scholar
15.Manin, Y., Correspondences, motives, and monoidal transformations, Math. USSRSb. 6 (1968), 439–470Google Scholar
16.Mumford, D., Abelian varieties. Tata Institute of Fundamental Research Studies in Mathematics 5, Oxford University Press, 1970Google Scholar
17.Murre, J., On the motive of an algebraic surface, J. Reine Angew. Math. 409 (1990), 190–204Google Scholar
18.Murre, J., On a conjectural filtration on the Chow groups of an algebraic variety: I and II. Indag. Math. (N.S.) 4, no. 2 (1993), 177–201CrossRefGoogle Scholar
19.Scholl, A. J., “Classical motives” in Motives, Proc. Symp. Pure Math. 55 part 1, AMS (1994), 189–205Google Scholar
20.Shermenev, A. M., The motive of an abelian variety. Funct. Anal. 8 (1974), 55–61Google Scholar