Local duality for representations of finite group schemes

Dave Benson; Srikanth B. Iyengar; Henning Krause; Julia Pevtsova

doi:10.1112/S0010437X19007061

Local duality for representations of finite group schemes

Dave Benson, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova

Mathematical Science

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6 Citations (Scopus)

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Abstract

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the p-local and p-torsion subcategories of the stable category, for each homogeneous prime ideal p in the cohomology ring of the group scheme.

Original language	English
Pages (from-to)	424-453
Number of pages	30
Journal	Compositio Mathematica
Volume	155
Issue number	2
Early online date	18 Feb 2019
DOIs	https://doi.org/10.1112/S0010437X19007061
Publication status	Published - Feb 2019

Bibliographical note

Acknowledgements. It is a pleasure to thank Tobias Barthel for detailed comments on an earlier version of this manuscript.

SBI was partly supported by NSF grant DMS-1503044 and JP was partly supported by NSF grants DMS-0953011 and DMS-1501146.

Keywords

Serre duality
local duality
finite group scheme
stable module category
Auslander-Reiten triangle

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AU - Pevtsova, Julia

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AB - A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the p-local and p-torsion subcategories of the stable category, for each homogeneous prime ideal p in the cohomology ring of the group scheme.

KW - Serre duality

KW - local duality

KW - finite group scheme

KW - stable module category

KW - Auslander-Reiten triangle

U2 - 10.1112/S0010437X19007061

DO - 10.1112/S0010437X19007061

M3 - Article

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EP - 453

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 2

ER -

Local duality for representations of finite group schemes

Abstract

Bibliographical note

Keywords

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