Abstract
Let G be a finite group and k an algebraically closed field of characteristic \(p > 0\). Let \({\mathcal H}\) be a collection of p-subgroups of G. We investigate the relative stable category \(\mathbf{stmod}_{\mathcal H}(kG)\) of finitely generated modules modulo \({\mathcal H}\)-projective modules. Triangles in this category correspond to \({\mathcal H}\)-split sequences. Hence, compared to the ordinary stable category, there are fewer triangles and more thick subcategories. Our interest is in the spectrum of the category and its relationship to the induction functor. In some cases, the spectrum is not noetherian.
To Dave Benson on the occasion of his 60th birthday.
Research partially supported by NSA grant H98230-15-1-0007 and by Simons Foundation grant 054813-01.
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Carlson, J.F. (2018). Thick Subcategories of the Relative Stable Category. In: Carlson, J., Iyengar, S., Pevtsova, J. (eds) Geometric and Topological Aspects of the Representation Theory of Finite Groups. PSSW 2016. Springer Proceedings in Mathematics & Statistics, vol 242. Springer, Cham. https://doi.org/10.1007/978-3-319-94033-5_2
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DOI: https://doi.org/10.1007/978-3-319-94033-5_2
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