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The Balmer spectrum of certain Deligne–Mumford stacks

Part of: Commutative algebra: Homological methods Representation theory of groups Connections with homological algebra and category theory Algebraic geometry: Foundations

Published online by Cambridge University Press:  24 May 2023

Eike Lau
Eike Lau*
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany lau@math.uni-bielefeld.de
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Abstract

We consider a Deligne–Mumford stack $X$ which is the quotient of an affine scheme $\operatorname {Spec}A$ by the action of a finite group $G$ and show that the Balmer spectrum of the tensor triangulated category of perfect complexes on $X$ is homeomorphic to the space of homogeneous prime ideals in the group cohomology ring $H^*(G,A)$.

Keywords

algebraic stacksperfect complexesBalmer spectrumtensor triangulated categories

MSC classification

Secondary: 13D09: Derived categories 14A20: Generalizations (algebraic spaces, stacks) 20C99: None of the above, but in this section 20J06: Cohomology of groups
Type
Research Article
Information
Compositio Mathematica , Volume 159 , Issue 6 , June 2023 , pp. 1314 - 1346
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Copyright
© 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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