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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2013, Volume 16, Issue 1, Pages 103–106 (Mi adm438)

RESEARCH ARTICLE

On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field

V. Nesteruk

Algebra and Logic Department, Mechanics and Mathematics Faculty, Ivan Franko National University of L’viv, 1, Universytetska str., Lviv, 79000, Ukraine

Abstract: In this note, we consider the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field. P. Bruin [1] defined this pairing over finite field $k$: $\mathrm{ker} \hat{\phi}(k) \; \times \; \mathrm{coker} (\phi(k)) \longrightarrow k^*$, and proved its perfectness over finite field. We prove perfectness of the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field, with help of the method, used by P. Bruin in the case of finite ground field [1].

Keywords: pseudofinite field, isogeny, Tate pairing associated to an isogeny.

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Bibliographic databases:
MSC: 12G99, 14H05, 14K02
Revised: 30.03.2013
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Citation: V. Nesteruk, “On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field”, Algebra Discrete Math., 16:1 (2013), 103–106

Citation in format AMSBIB
\Bibitem{Nes13} \by V.~Nesteruk \paper On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field \jour Algebra Discrete Math. \yr 2013 \vol 16 \issue 1 \pages 103--106 \mathnet{http://mi.mathnet.ru/adm438} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184702}