Stacks of group representations
By Paul Balmer. 2013
59 citations recorded by the source corpus.
We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group G, the derived and the stable categories of representations of a subgroup H can be constructed out of the corresponding category for G by a purely triangulated-categorical construction, analogous to etale extension in algebraic geometry. In the case of finite groups, we then use descent methods to investigate when modular representations of the subgroup H can be extended to G. We show that the presheaves of plain, derived and stable representations all form stacks on the category of finite G-sets (or the orbit category of G), with respect to a suitable Grothendieck topology that we call the sipp topology. When H contains a Sylow subgroup of G, we use sipp Cech cohomology to describe the kernel and the image of the homomorphism T (G)→ T (H), where T (−) denotes the group of endotrivial representations.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c8c29279b3c684336c5fdaf094d1dfe5f96f2095
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Citations in the corpus
- The Galois group of a stable homotopy theory (2014, background): “We state this formally as a proposition (compare [5,7]).”
- Nilpotence and descent in equivariant stable homotopy theory (2015, background): “Theorem 5.32 (Cf. Balmer–Dell’Ambrogio–Sanders [9]).”