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

被引：0

作者：

Nesteruk, Volodymyr ^{[1
]}

机构：

[1] Ivan Franko Natl Univ, Mech & Math Fac, Algebra & Log Dept, Univ Str, UA-79000 Lvov, Ukraine

来源：

ALGEBRA & DISCRETE MATHEMATICS | 2013年 / 16卷 / 01期

关键词：

pseudofinite field; isogeny; Tate pairing associated to an isogeny;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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: ker phi(k) x raker (phi(k)) -> k* arid proved its perfectness oVer finite field, prove perfectness of the Tate pairing associated to an isogeny between abelian varieties over pseudofirtite field, with help of the method, used by P. Bruin in the case of -finite ground field [1]

引用

页码：103 / 106

页数：4

共 47 条

[1] The Tate pairing for Abelian varieties over finite fields
Bruin, Peter
JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2011, 23 (02): : 323 - 328
[2] The Cassels-Tate pairing on polarized abelian varieties
Poonen, B
Stoll, M
ANNALS OF MATHEMATICS, 1999, 150 (03) : 1109 - 1149
[3] Isogeny classes of abelian varieties over function fields
Zarhin, Yuri G.
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2008, 96 : 312 - 334
[4] ISOGENY CLASSES OF ABELIAN VARIETIES OVER FINITE FIELDS
HONDA, T
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1968, 20 (1-2) : 83 - +
[5] Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian
Schaefer, EF
Wetherell, JL
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[6] Isogeny classes and endomorphism algebras of abelian varieties over finite fields
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IZVESTIYA MATHEMATICS, 2023, 87 (03) : 469 - 487
[7] On a number of isogeny classes of simple abelian varieties over finite fields
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[8] Cyclic abelian varieties over finite fields in ordinary isogeny classes
Giangreco-Maidana, Alejandro J.
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[9] On a number of isogeny classes of simple abelian varieties over finite fields
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[10] The Tate conjecture for certain abelian varieties over finite fields
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ACTA ARITHMETICA, 2001, 100 (02) : 135 - 166

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