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Mat. Sb. (N.S.), 1979, Volume 110(152), Number 1(9), Pages 88–101 (Mi msb2426)  

This article is cited in 1 scientific paper (total in 1 paper)

On elliptic curves over pseudolocal fields

V. I. Andriichuk


Abstract: In this paper it is shown that for pseudolocal fields there is a natural analog of the Tate–Shafarevich duality for elliptic curves, taking the following form:
Theorem. If $A$ is an elliptic curve defined over the pseudolocal field $k$, whose residue field has characteristic not equal to $2$ or $3$, then the Tate–Shafarevich pairing
$$ H^1(k,A)\times A_k\to Q/Z $$
is left nondegenerate
.
Bibliography: 11 titles.

Full text: PDF file (1360 kB)
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English version:
Mathematics of the USSR-Sbornik, 1981, 38:1, 83–94

Bibliographic databases:

UDC: 513.6
MSC: Primary 14K07; Secondary 12L10
Received: 03.08.1978

Citation: V. I. Andriichuk, “On elliptic curves over pseudolocal fields”, Mat. Sb. (N.S.), 110(152):1(9) (1979), 88–101; Math. USSR-Sb., 38:1 (1981), 83–94

Citation in format AMSBIB
\Bibitem{And79}
\by V.~I.~Andriichuk
\paper On elliptic curves over pseudolocal fields
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 110(152)
\issue 1(9)
\pages 88--101
\mathnet{http://mi.mathnet.ru/msb2426}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=548518}
\zmath{https://zbmath.org/?q=an:0464.14006|0444.14028}
\transl
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 1
\pages 83--94
\crossref{https://doi.org/10.1070/SM1981v038n01ABEH001223}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981LB83400006}


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    This publication is cited in the following articles:
    1. Banakh T.O., Bogomolov F.A., Gatalevych A.I., Guran I.J., Ishchuk Yu.B., Komarnytskyi M.Ya., Kuz I.S., Melnyk I.O., Petrychkovych V.M., Prytula Ya.G., Romaniv O.M., Skaskiv O.B., Stakhiv L.L., Sullym G.T., Zabavskyi B.V., Zelisko V.P., Zarichnyi M.M., “Obituary: Vasyl Ivanovych Andriychuk (18.09.1948-7.07.2012)”, Cent. Eur. J. Math., 11:9 (2013), 1547–1551  crossref  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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