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This article is cited in 14 scientific papers (total in 14 papers)
Families of algebraic varieties and invariant cycles
G. A. Mustafin
Abstract:
This paper studies monodromy-invariant cycles in the cohomology of fibers of a family of algebraic varieties. It is shown that the localization of invariant cycles in a neighborhood of a degeneration of the family is a morphism of Hodge structures. An application of this result is the geometric analogue of the Mumford–Tate conjecture for families with strong degenerations. A large class of nonconstant abelian schemes for which the geometric analogue of the Mumford–Tate conjecture holds is constructed.
Bibliography: 29 titles.
Received: 16.11.1983
Citation:
G. A. Mustafin, “Families of algebraic varieties and invariant cycles”, Math. USSR-Izv., 27:2 (1986), 251–278
Linking options:
https://www.mathnet.ru/eng/im1373https://doi.org/10.1070/IM1986v027n02ABEH001177 https://www.mathnet.ru/eng/im/v49/i5/p948
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