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Mathematics of the USSR-Izvestiya, 1992, Volume 39, Issue 1, Pages 829–853
DOI: https://doi.org/10.1070/IM1992v039n01ABEH002228 (Mi im991) 		 
This article is cited in 6 scientific papers (total in 6 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
English version PDF (1401 kB) Citations (6)
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DOI: https://doi.org/10.1070/IM1992v039n01ABEH002228
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.
Received: 08.08.1990
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1991, Volume 55, Issue 4, Pages 851–876
Bibliographic databases:
Document Type: Article
UDC: 512.7
MSC: Primary 11G40, 11G18, 11R39; Secondary 14G35
Language: English
Original paper language: Russian
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
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\yr 1991
\vol 55
\issue 4
\pages 851--876
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\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 39
\issue 1
\pages 829--853
\crossref{https://doi.org/10.1070/IM1992v039n01ABEH002228}
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    • This publication is cited in the following 6 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:645
    Russian version PDF:183
    English version PDF:23
    References:41
    First page:2
     
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