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Russian Mathematical Surveys, 1971, Volume 26, Issue 6, Pages 7–78
DOI: https://doi.org/10.1070/RM1971v026n06ABEH001272 (Mi rm5277) 		 
This article is cited in 60 scientific papers (total in 61 papers)

Cyclotomic fields and modular curves

Yu. I. Manin
English version PDF (3274 kB) Citations (61) Russian version article
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DOI: https://doi.org/10.1070/RM1971v026n06ABEH001272
Abstract: The first chapter of this article contains an exposition of the work of Iwasawa and Mazur on the arithmetic of Abelian varieties over cyclotomic fields. The study of questions arising here leads us in the second chapter to the use of the zeta-function apparatus, and the conjectures of Weil and Birch–Swinnerton-Dyer; this permits us to obtain conditional formulae for the order of the Tate–Shafarevich group.
Received: 31.05.1971
Bibliographic databases:
Document Type: Article
UDC: 517.5+519.4
MSC: 11T22, 11R60, 11R34, 12G05, 11G40, 14G10
Language: English
Original paper language: Russian
Citation: Yu. I. Manin, “Cyclotomic fields and modular curves”, Russian Math. Surveys, 26:6 (1971), 7–78
Citation in format AMSBIB
\Bibitem{Man71}
\by Yu.~I.~Manin
\paper Cyclotomic fields and modular curves
\jour Russian Math. Surveys
\yr 1971
\vol 26
\issue 6
\pages 7--78
\mathnet{http://mi.mathnet.ru//eng/rm5277}
\crossref{https://doi.org/10.1070/RM1971v026n06ABEH001272}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=401653}
\zmath{https://zbmath.org/?q=an:0241.14014}
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    • This publication is cited in the following 61 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
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    Abstract page:1388
    Russian version PDF:760
    English version PDF:107
    References:96
    First page:4
     
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