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arXiv · 2307.16271

Lattices over finite group schemes and stratification

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

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BibTeXRIS

Tobias Barthel, Dave Benson, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova. 2023-07-30. Lattices over finite group schemes and stratification. https://arxiv.org/abs/2307.16271

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