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ЖУРНАЛЫ // Algebra and Discrete Mathematics // Архив

Algebra Discrete Math., 2013, том 16, выпуск 1, страницы 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

Аннотация: 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].

Ключевые слова: pseudofinite field, isogeny, Tate pairing associated to an isogeny.

MSC: 12G99, 14H05, 14K02

Поступила в редакцию: 13.02.2012
Исправленный вариант: 30.03.2013

Язык публикации: английский



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