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Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 4, Pages 851–876 (Mi izv991)  

This article is cited in 2 scientific papers (total in 2 papers)

Finiteness of Ш over totally real fields

V. A. Kolyvagina, D. Yu. Logachevb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: Kolyvagin's method for the proof of the finiteness of Ш is extended to abelian varieties with real multiplication, of $L$-rank 0, defined over totally real fields, if they are factors of the Jacobians of Shimura curves. The finiteness of Ш for such a variety is proved, starting from the conditions that a Heegner point on it is not a torsion point.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 39:1, 829–853

Bibliographic databases:

UDC: 512.7
MSC: Primary 11G40, 11G18, 11R39; Secondary 14G35
Received: 08.08.1990

Citation: V. A. Kolyvagin, D. Yu. Logachev, “Finiteness of Ш over totally real fields”, Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991), 851–876; Math. USSR-Izv., 39:1 (1992), 829–853

Citation in format AMSBIB
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\by V.~A.~Kolyvagin, D.~Yu.~Logachev
\paper Finiteness of {\it Ш\/} over totally real fields
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
\issue 4
\pages 851--876
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\zmath{https://zbmath.org/?q=an:0791.14019}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..39..829K}
\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 39
\issue 1
\pages 829--853
\crossref{https://doi.org/10.1070/IM1992v039n01ABEH002228}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JQ84600007}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. Yu. Logachev, “Reduction of a problem of finiteness of Tate-Shafarevich group to a result of Zagier type”, Dalnevost. matem. zhurn., 9:1-2 (2009), 105–130  mathnet  elib
    2. Werner Bley, “Numerical Evidence for the Equivariant Birch and Swinnerton-Dyer Conjecture”, Experimental Mathematics, 20:4 (2011), 426  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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