On the Galois and Flat Cohomology of Unipotent Algebraic Groups over Local and Global Function Fields

被引：0

作者：

Rosengarten, Zev ^{[1
]}

Tan, Nguyen Duy ^{[2
]}

Thang, Nguyen Quoc ^{[3
]}

机构：

[1] Hebrew Univ Jerusalem, Einstein Inst Math, IL-9190401 Givat Ram, Jerusalem, Israel

[2] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, 1 Dai Co Viet, Hanoi, Vietnam

[3] VAST, Inst Math, 18 Hoang Quoc Viet, CauGiay 10307, Hanoi, Vietnam

来源：

MICHIGAN MATHEMATICAL JOURNAL | 2024年 / 74卷 / 04期

关键词：

D O I：

10.1307/mmj/20216162

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let k be a field of positive characteristic p with degree of imperfection 1 and a nontrivial discrete valuation. We show that the Galois and flat cohomology of unipotent k-groups over k of dimension < p - 1 are finite (in fact, trivial) if and only if they are k-split. We give some examples to show that the bound p - 1 is best possible and present several applications to local-global principles.

引用

页码：721 / 741

页数：21

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