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Stratification for module categories of finite group schemes


Authors: Dave Benson, Srikanth B. Iyengar, Henning Krause and Julia Pevtsova
Journal: J. Amer. Math. Soc. 31 (2018), 265-302
MSC (2010): Primary 16G10; Secondary 20G10, 20J06
DOI: https://doi.org/10.1090/jams/887
Published electronically: August 15, 2017
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Abstract: The tensor ideal localizing subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning the structure of the stable module category and the behavior of support and cosupport under restriction and induction are presented.


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Additional Information

Dave Benson
Affiliation: Institute of Mathematics, University of Aberdeen, King’s College, Aberdeen AB24 3UE, Scotland, United Kingdom

Srikanth B. Iyengar
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112

Henning Krause
Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany

Julia Pevtsova
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: julia@math.washington.edu

DOI: https://doi.org/10.1090/jams/887
Keywords: Cosupport, finite group scheme, localizing subcategory, support, thick subcategory
Received by editor(s): November 3, 2015
Received by editor(s) in revised form: April 5, 2016, April 24, 2017, and June 16, 2017
Published electronically: August 15, 2017
Additional Notes: The second author was partly supported by NSF grant DMS 1503044.
The fourth author was partly supported by NSF grant DMS 0953011.
Article copyright: © Copyright 2017 American Mathematical Society

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