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Generalized Siegel Modular Forms and Cohomology of Locally Symmetric Varieties

Published online by Cambridge University Press:  20 November 2018

Min Ho Lee
Min Ho Lee*
Affiliation:
Department of Mathematics University of Northern Iowa Cedar Falls, IA U.S.A. 50614, e-mail: lee@math.uni.edu
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Abstract

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We generalize Siegel modular forms and construct an exact sequence for the cohomology of locally symmetric varieties which plays the role of the Eichler-Shimura isomorphism for such generalized Siegel modular forms.

Keywords

Primary: 11F46Secondary: 11F7522E40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 1 , 01 March 1997 , pp. 72 - 80
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Bayer, P. and Neukirch, J., On automorphic forms and Hodge theory, Math. Ann. 257 (1981), 137–155.Google Scholar
2. Baily, W. and Borel, A., Compactification of arithmetic quotients of bounded symmetric domains, Ann. Math. 84 (1966), 442–528.Google Scholar
3. Hartshorne, R., Algebraic geometry, Springer-Verlag, New York, 1977.Google Scholar
4. Kuga, M., Fiber varieties over a symmetric space whose fibers are abelian varieties I, II, Lect. Notes, Univ. Chicago, 1963/64.Google Scholar
5. Lee, M. H., Mixed cusp forms and holomorphic forms on elliptic varieties, Pacific J. Math. 132 (1988), 363–370.Google Scholar
6. Lee, M. H., Conjugates of equivariant holomorphic maps of symmetric domains, Pacific J. Math. 149 (1991), 127–144.Google Scholar
7. Lee, M. H., Mixed cusp forms and Poincaré series, RockyMountain J. Math. 23 (1993), 1009–1022.Google Scholar
8. Lee, M. H., Mixed automorphic forms and Hodge structures, Panamer.Math. J. (2) 4 (1994), 89–113.Google Scholar
9. Lee, M. H., Mixed Siegel modular forms and Kuga fiber varieties, Illinois J. Math. 38 (1994), 692–700.Google Scholar
10. Lee, M. H. , Mixed automorphic vector bundles on Shimura varieties, Pacific J. Math. 173 (1996), 105–126.Google Scholar
11. Nenashev, A., Siegel modular forms and cohomology, Math. USSR Izvestiya 29 (1987), 559–586.Google Scholar
12. Satake, I., Algebraic structures of symmetric domains, Princeton Univ. Press, Princeton, 1980.Google Scholar
13. Wells, R., Jr., Differential analysis on complex manifolds, Springer-Verlag, New York, 1980.Google Scholar