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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Antiholomorphic involutions of analytic families of abelian varieties

Author: Allan Adler
Journal: Trans. Amer. Math. Soc. 254 (1979), 69-94
MSC: Primary 10D20; Secondary 14K22
MathSciNet review: 539908
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Abstract: In this paper, we investigate antiholomorphic involutions of Kuga-Satake analytic families of polarized abelian varieties V. A complete set of invariants of the Aut(V)-conjugacy classes of antiholomorphic involutions of V is obtained. These invariants are expressed as cohomological invariants of the arithmetic data defining V. In the last section, the fibre varieties of Kuga-Satake type belonging to totally indefinite quaternion division algebras over totally real fields are investigated in more detail, and the cohomological invariants are related to results of Steve Kudla. The group of holomorphic sections of V is computed for this case. It is also shown that in general the fibre structure of V is intrinsic.

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Keywords: Symmetric space, antiholomorphic, cohomology, cohomology with nonabelian coefficients, quaternion algebra, totally indefinite, algebraic number field, totally real, fibre variety, maximal order, ideal class group, connection, properly discontinuously
Article copyright: © Copyright 1979 American Mathematical Society