Residue maps, Azumaya algebras, and buildings

Published 6 Mar 2023 in math.RA, math.GR, and math.NT | (2303.03175v2)

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.

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Igor A. Rapinchuk

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