A Tate duality theorem for local Galois symbols II; The semi-abelian case

JOURNAL OF NUMBER THEORY

卷:204

Article

Gazaki, Evangelia¹ 

[1] Univ Michigan, Dept Math, 3823 East Hall,530 Church St, Ann Arbor, MI 48109 USA

关键词: Semi-abelian varieties;    Somekawa K-groups;    Galois cohomology;    Local fields;   

DOI  :  10.1016/j.jnt.2019.04.017

来源: Elsevier

【 摘 要 】

This paper is a continuation to [Gaz17]. For every integer n >= 1, we consider the generalized Galois symbol K(k; G(1), G(2))/n ->(sn) H-2 (k, G(1)[n]circle times G(2)[n]), where k is a finite extension of Q(p), G(1), G(2) are semi-abelian varieties over k and K(k; G(1), G(2) ) is the Somekawa K-group attached to G(1), G(2). Under some mild assumptions, we describe the exact annihilator of the image of s(n) under the Tate duality perfect pairing, H-2 (k, G(1)[n]circle times G(2)[n])X H-0 (k,Hom(G(1)[n]circle times G(2) [n], mu(n)))-> Z/n. An important special case is when both G(1), G(2) are abelian varieties with split semistable reduction. In this case we prove a finiteness result, which gives an application to zero-cycles on abelian varieties and products of curves. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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