September 2024 On the Galois and Flat Cohomology of Unipotent Algebraic Groups over Local and Global Function Fields. II
Zev Rosengarten, Nguyễn Duy Tân, Nguyễn Quốc Thắng
Michigan Math. J. 74(4): 721-741 (September 2024). DOI: 10.1307/mmj/20216162

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 <p1 are finite (in fact, trivial) if and only if they are k-split. We give some examples to show that the bound p1 is best possible and present several applications to local-global principles.

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Zev Rosengarten. Nguyễn Duy Tân. Nguyễn Quốc Thắng. "On the Galois and Flat Cohomology of Unipotent Algebraic Groups over Local and Global Function Fields. II." Michigan Math. J. 74 (4) 721 - 741, September 2024. https://doi.org/10.1307/mmj/20216162

Information

Received: 12 November 2021; Revised: 18 August 2022; Published: September 2024
First available in Project Euclid: 2 September 2024

Digital Object Identifier: 10.1307/mmj/20216162

Keywords: 11E72 , 12F05 , 12F15 , 20G10

Rights: Copyright © 2024 The University of Michigan

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Vol.74 • No. 4 • September 2024
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