Residue maps, Azumaya algebras, and buildings
Rings and Algebras
2024-02-28 v2 Group Theory
Number Theory
Abstract
The goal of this note is to give an explicit formula for the residues of twists of the matrix algebra in terms of the twisting cocycle. Combined with the Fixed Point Theorem for actions of finite groups on affine buildings, this leads to a quick proof of the well-known characterization of unramified algebras in terms of Azumaya algebras.
Keywords
Cite
@article{arxiv.2303.03175,
title = {Residue maps, Azumaya algebras, and buildings},
author = {Igor A. Rapinchuk},
journal= {arXiv preprint arXiv:2303.03175},
year = {2024}
}
Comments
Corrections and clarifications based on referee's comments