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 CantorBendixson rank of X.
Injective dimension of sheaves of rational vector spaces
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