Stratification and π-cosupport: finite groups

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

doi:10.1007/s00209-017-1853-8

Stratification and π-cosupport: finite groups

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

Mathematical Science

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3 Citations (Scopus)

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Abstract

We introduce the notion of ππ -cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give a new proof of the classification of tensor ideal localising subcategories. In a sequel to this paper, we carry out the corresponding classification for finite group schemes.

Original language	English
Pages (from-to)	947-965
Number of pages	19
Journal	Mathematische Zeitschrift
Volume	287
Issue number	3-4
Early online date	23 Feb 2017
DOIs	https://doi.org/10.1007/s00209-017-1853-8
Publication status	Published - Dec 2017

Bibliographical note

Acknowledgements
Part of this article is based on work supported by the National Science Foundation under Grant No. 0932078000, while DB, SBI, and HK were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the 2012–2013 Special Year in Commutative Algebra. The authors thank the Centre de Recerca Matemàtica, Barcelona, for hospitality during a visit in April 2015 that turned out to be productive and pleasant. SBI and JP were partly supported by NSF Grants DMS-1503044 and DMS-0953011, respectively. We are grateful to Eric Friedlander for comments on an earlier version of this paper.

Keywords

cosupport
stable module category
finite group scheme
localising subcategory
support
thick subcategory

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Accepted Manuscript
This is a post-peer-review, pre-copyedit version of an article published in Mathematische Zeitschrift. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00209-017-1853-8
Accepted author manuscript, 337 KBLicence: Unspecified

Cite this

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abstract = "We introduce the notion of ππ -cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give a new proof of the classification of tensor ideal localising subcategories. In a sequel to this paper, we carry out the corresponding classification for finite group schemes.",

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N1 - Acknowledgements Part of this article is based on work supported by the National Science Foundation under Grant No. 0932078000, while DB, SBI, and HK were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the 2012–2013 Special Year in Commutative Algebra. The authors thank the Centre de Recerca Matemàtica, Barcelona, for hospitality during a visit in April 2015 that turned out to be productive and pleasant. SBI and JP were partly supported by NSF Grants DMS-1503044 and DMS-0953011, respectively. We are grateful to Eric Friedlander for comments on an earlier version of this paper.

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KW - finite group scheme

KW - localising subcategory

KW - support

KW - thick subcategory

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JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

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ER -

Stratification and π-cosupport: finite groups

Abstract

Bibliographical note

Keywords

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