Injective dimension of sheaves of rational vector spaces

摘要

The Cantor-Bendixson rank of a topological space X is a measure of the complexity of the topology of X. We will be interested primarily in the case that the space is profinite: Hausdorff, compact and totally disconnected. In this paper, we prove that the injective dimension of the abelian category of sheaves of Q-modules over a profinite space X is determined by the Cantor Bendixson rank of X. Crown Copyright (C) 2018 Published by Elsevier B.V. All rights reserved.