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

Zev Rosengarten; Nguyên Duy Tân; Nguyên Quốc Thang

doi:10.1307/mmj/20216162

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

Zev Rosengarten
, Nguyên Duy Tân
, Nguyên Quốc Thang

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	721-741
Number of pages	21
Journal	Michigan Mathematical Journal
Volume	74
Issue number	4
DOIs	https://doi.org/10.1307/mmj/20216162
State	Published - Sep 2024

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© 2024 University of Michigan. All rights reserved.

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10.1307/mmj/20216162

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

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