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Mathematics of the USSR-Izvestiya, 1986, Volume 27, Issue 2, Pages 251–278
DOI: https://doi.org/10.1070/IM1986v027n02ABEH001177 (Mi im1373) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Families of algebraic varieties and invariant cycles

G. A. Mustafin
English version PDF (1879 kB) Citations (14)
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DOI: https://doi.org/10.1070/IM1986v027n02ABEH001177
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
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1985, Volume 49, Issue 5, Pages 948–978
Bibliographic databases:
UDC: 513.6
MSC: Primary 14K10, 14C30; Secondary 14K15, 14L32, 17B10
Language: English
Original paper language: Russian
Citation: G. A. Mustafin, “Families of algebraic varieties and invariant cycles”, Izv. Akad. Nauk SSSR Ser. Mat., 49:5 (1985), 948–978; Math. USSR-Izv., 27:2 (1986), 251–278
Citation in format AMSBIB
\Bibitem{Mus85}
\by G.~A.~Mustafin
\paper Families of algebraic varieties and invariant cycles
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 5
\pages 948--978
\mathnet{http://mi.mathnet.ru/im1373}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=810526}
\zmath{https://zbmath.org/?q=an:0633.14012}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 27
\issue 2
\pages 251--278
\crossref{https://doi.org/10.1070/IM1986v027n02ABEH001177}
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  • https://www.mathnet.ru/eng/im/v49/i5/p948
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:470
    Russian version PDF:137
    English version PDF:34
    References:97
    First page:2
     
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