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Mat. Sb. (N.S.), 1970, Volume 83(125), Number 3(11), Pages 474–484 (Mi msb3523)  

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

On the Galois cohomology of elliptic curves defined over a local field

O. N. Vvedenskii


Abstract: In this article we calculate the group of principal homogeneous spaces over elliptic curves defined over a complete discretely normed field with algebraically closed residue field of characteristic $p>3$ and belonging to types $(c 4)$, $(c 5)$ in the classification of A. Neron. The result of our calculations refutes Neron's earlier statement that the group of principal homogeneous spaces over curves of type $(c)$ is trivial. Moreover the calculation of the fundamental group of the proalgebraic group of the points on these curves that are rational over the ground field supports (in this case) the conjecture of I. R. Shafarevich concerning the duality of the group of principal homogeneous spaces and the character group of the fundamental group.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1970, 12:3, 477–488

Bibliographic databases:

UDC: 513.015.7
MSC: 11S25, 12G05, 11E72, 12J05, 20K30, 11G07
Received: 09.03.1970

Citation: O. N. Vvedenskii, “On the Galois cohomology of elliptic curves defined over a local field”, Mat. Sb. (N.S.), 83(125):3(11) (1970), 474–484; Math. USSR-Sb., 12:3 (1970), 477–488

Citation in format AMSBIB
\Bibitem{Vve70}
\by O.~N.~Vvedenskii
\paper On~the Galois cohomology of elliptic curves defined over a~local field
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 83(125)
\issue 3(11)
\pages 474--484
\mathnet{http://mi.mathnet.ru/msb3523}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=279107}
\zmath{https://zbmath.org/?q=an:0213.23003}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 12
\issue 3
\pages 477--488
\crossref{https://doi.org/10.1070/SM1970v012n03ABEH000932}


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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. O. N. Vvedenskii, “On quasi-local “class fields” of elliptic curves. I”, Math. USSR-Izv., 10:5 (1976), 913–936  mathnet  crossref  mathscinet  zmath
    2. Qing Liu, Dino Lorenzini, Michel Raynaud, “Néron models, Lie algebras, and reduction of curves of genus one”, Invent math, 157:3 (2004), 455  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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