Lattices over finite group schemes and stratification

Barthel, Tobias; Benson, Dave; Iyengar, Srikanth B.; Krause, Henning; Pevtsova, Julia

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Lattices over finite group schemes and stratification

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Barthel, Tobias
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2307.16271
(Preprint)

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2307.16271.pdf
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Barthel, T., Benson, D., Iyengar, S. B., Krause, H., & Pevtsova, J. (submitted). Lattices over finite group schemes and stratification.

Cite as: https://hdl.handle.net/21.11116/0000-000F-5E79-1

Abstract

This work concerns representations of a finite flat group scheme G, defined over a noetherian commutative ring R. The focus is on lattices, namely, finitely generated G-modules that are projective as R-modules, and on the full subcategory of all G-modules projective over R generated by the lattices. The stable category of such G-modules is a rigidly-compactly generated, tensor triangulated category. The main result is that this stable category is stratified and costratified by the natural action of the cohomology ring of G. Applications include formulas for computing the support and cosupport of tensor products and the module of homomorphisms, and a classification of the thick ideals in the stable category of lattices.