固定循环扩展中塔特-沙法列维奇群的无界性

IF 1 3区数学 Q1 MATHEMATICS Mathematische Zeitschrift Pub Date : 2024-06-22 DOI:10.1007/s00209-024-03527-3

Yi Ouyang, Jianfeng Xie

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摘要

在本文中，我们证明了两个关于在全局域的固定非小循环扩展L/K中的无方变体的塔特-沙法列维奇群的无界性结果，首先是在K是数域且无方变体是椭圆曲线的情况下，其次是在K是全局域、[L : K]是2幂且无方变体是主极化的情况下。

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Unboundedness of Tate–Shafarevich groups in fixed cyclic extensions

In this paper we prove two unboundedness results about the Tate–Shafarevich groups of abelian varieties in a fixed nontrivial cyclic extension L/K of global fields, firstly in the case that K is a number field and the abelian varieties are elliptic curves, secondly in the case that K is a global field, [L : K] is a 2-power and the abelian varieties are principally polarized.

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