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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4 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

Keywords

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

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Accepted ManuscriptAccepted author manuscript, 342 KBLicence: Other

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title = "Local duality for representations of finite group schemes",

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.",

keywords = "Serre duality, local duality, finite group scheme, stable module category, Auslander-Reiten triangle",

author = "Dave Benson and Iyengar, {Srikanth B.} and Henning Krause and Julia Pevtsova",

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.",

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language = "English",

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T1 - Local duality for representations of finite group schemes

AU - Benson, Dave

AU - Iyengar, Srikanth B.

AU - Krause, Henning

AU - Pevtsova, Julia

N1 - 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.

PY - 2019/2

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N2 - 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.

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

VL - 155

SP - 424

EP - 453

JO - Compositio Mathematica

JF - Compositio Mathematica

SN - 1570-5846

IS - 2

ER -

Local duality for representations of finite group schemes

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Keywords

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