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

The Hebrew University of Jerusalem

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

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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1307/mmj/20216162

Cite this

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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