Galois cohomology of real quasi-connected reductive groups
Abstract
By a quasi-connected reductive group (a term of Labesse) over an arbitrary field we mean an almost direct product of a connected semisimple group and a quasi-torus (a smooth group of multiplicative type). We show that a linear algebraic group is quasi-connected reductive if and only if it is isomorphic to a smooth normal subgroup of a connected reductive group. We compute the first Galois cohomology set H^1(R,G) of a quasi-connected reductive group G over the field R of real numbers in terms of a certain action of a subgroup of the Weyl group on the Galois cohomology of a fundamental quasi-torus of G.
Keywords
Cite
@article{arxiv.2103.04654,
title = {Galois cohomology of real quasi-connected reductive groups},
author = {Mikhail Borovoi and Andrei A. Gornitskii and Zev Rosengarten},
journal= {arXiv preprint arXiv:2103.04654},
year = {2021}
}
Comments
Version 1: 9 pages. Version 2: 12 pages. Version 2 supersedes arXiv:2108.05694. Starting this version, we consider quasi-connected reductive groups over a field of *arbitrary characteristic*. A new coauthor has been added