Tate Duality In Positive Dimension over Function Fields

IF 2 4区数学 Q1 MATHEMATICS

Memoirs of the American Mathematical Society Pub Date : 2023-10-01 DOI:10.1090/memo/1444

Zev Rosengarten

引用次数: 10

Abstract

We extend the classical duality results of Poitou and Tate for finite discrete Galois modules over local and global fields (local duality, nine-term exact sequence, etc.) to all affine commutative group schemes of finite type, building on the recent work of Česnavičius (“Poitou-Tate without restrictions on the order,” 2015) extending these results to all finite commutative group schemes. We concentrate mainly on the more difficult function field setting, giving some remarks about the number field case along the way.

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函数域上正维的Tate对偶性

我们将局部和全局域上有限离散Galois模的经典对偶结果(局部对偶，九项精确序列等)推广到有限类型的所有仿射交换群方案，建立在Česnavičius最近的工作(“Poitou-Tate without restrictions on the order，”2015)的基础上，将这些结果推广到所有有限交换群方案。我们主要集中在较困难的函数域设置上，并在此过程中对数字域的情况做了一些说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Memoirs of the American Mathematical Society 数学-数学

CiteScore

3.50

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.