Duality Theorems for Abelian Varieties over $Z_{p}$-extensions
Duality Theorems for Abelian Varieties over $Z_{p}$-extensions
复制标题
$Z_{p}$-扩展上的阿贝尔簇的对偶定理
DOI：
10.2969/aspm/01710471
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
Kay Wingberg
中科院分区：
文献类型：
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作者：
Kay Wingberg
本文给出了交换簇A在k的ZP-扩张k00的零点上的代数数域k上的p-进高对的定义，证明了存在从p-Selmer群的Pontrjagin对偶的A-扭子模TAH1(00，d(P))*到对偶交换簇A‘的相应模的伴随a的映射.这里A表示Zp上的Gal(k00/k)的完全群环，p是素数，其中A有良好的约化。D表示定义在0~k00的整数环上的Nelon模型。更一般地，对于I>；O，存在正则映射
Our concern in this paper is to define p-adic height pairings for an abelian variety A over an algebraic number field k on the niveau of a ZP-extension k 00 of k. We will show that there exists a map from the A-torsion submodule TAH1(0 00 , d(p))* of the Pontrjagin dual of the p-Selmer group to the adjoint a of the corresponding module for the dual abelian variety A'. Here A denotes the completed group ring of Gal(k00 /k) over ZP and p is a prime number where A has good reduction. d denotes the Neron model defined over the ring of integers 0~ of k 00 • More generally, for i>O there are canonical maps