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Cohomology of Complex Torus Bundles Associated to Cocycles

Published online by Cambridge University Press:  20 November 2018

Min Ho Lee*
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, U.S.A. email: [email protected]
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Abstract

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Equivariant holomorphic maps of Hermitian symmetric domains into Siegel upper half spaces can be used to construct families of abelian varieties parametrized by locally symmetric spaces, which can be regarded as complex torus bundles over the parameter spaces. We extend the construction of such torus bundles using 2-cocycles of discrete subgroups of the semisimple Lie groups associated to the given symmetric domains and investigate some of their properties. In particular, we determine their cohomology along the fibers.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2003

References

[1] Choie, Y. and Lee, M. H., Mixed Siegel modular forms and special values of certain Dirichlet series. Monatsh.Math. 131(2000), 109122.Google Scholar
[2] Hall, M. Jr., The theory of groups. Macmillan, New York, 1959.Google Scholar
[3] Hartshorne, R., Algebraic geometry. Springer-Verlag, Heidelberg, 1977.Google Scholar
[4] Kuga, M., Fiber varieties over a symmetric space whose fibers are abelian varieties I, II. Univ. of Chicago, Chicago, 1963/64.Google Scholar
[5] Lange, H. and Birkenhake, Ch., Complex abelian varieties. Springer-Verlag, Berlin, 1992.Google Scholar
[6] Lee, M. H., Mixed automorphic vector bundles on Shimura varieties. Pacific J. Math. 173(1996), 105126.Google Scholar
[7] Lee, M. H. and Suh, D. Y., Torus bundles over locally symmetric varieties associated to cocycles of discrete groups. Monatsh. Math. 59(2000), 127141.Google Scholar
[8] Milne, J. S., Canonical models of (mixed) Shimura varieties and automorphic vector bundles. In: Automorphic forms, Shimura Varieties and L-functions, Vol. 1, Academic Press, Boston, 1990, 283414.Google Scholar
[9] Satake, I., Algebraic structures of symmetric domains. Princeton Univ. Press, Princeton, 1980.Google Scholar