The prime spectra of relative stable module categories
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- by Shawn Baland, Alexandru Chirvasitu and Greg Stevenson PDF
- Trans. Amer. Math. Soc. 371 (2019), 489-503 Request permission
Abstract:
For a finite group $G$ and an arbitrary commutative ring $R$, Broué has placed a Frobenius exact structure on the category of finitely generated $RG$-modules by taking the exact sequences to be those that split upon restriction to the trivial subgroup. The corresponding stable category is then tensor triangulated. In this paper we examine the case $R=S/t^n$, where $S$ is a discrete valuation ring having uniformising parameter $t$. We prove that the prime ideal spectrum (in the sense of Balmer) of this ‘relative’ version of the stable module category of $RG$ is a disjoint union of $n$ copies of that for $kG$, where $k$ is the residue field of $S$.References
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Additional Information
- Shawn Baland
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- MR Author ID: 953757
- Email: shawn.baland@gmail.com
- Alexandru Chirvasitu
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- Address at time of publication: Department of Mathematics, University at Buffalo, Buffalo, New York 14260
- MR Author ID: 868724
- Email: achirvas@buffalo.edu
- Greg Stevenson
- Affiliation: Universität Bielefeld, Fakultät für Mathematik, BIREP Gruppe, Postfach 10 01 31, 33501 Bielefeld, Germany
- Address at time of publication: School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QQ, Scotland
- MR Author ID: 1000578
- Email: gregory.stevenson@glasgow.ac.uk
- Received by editor(s): January 18, 2016
- Received by editor(s) in revised form: April 19, 2017
- Published electronically: July 20, 2018
- Additional Notes: The first and third authors are grateful to Universität Bielefeld and were partially supported by CRC 701 during a portion of the period in which this research was conducted.
The second author was partially supported by the NSF grant DMS-1565226.
The third author was also partially supported by a fellowship from the Alexander von Humboldt Foundation. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 489-503
- MSC (2010): Primary 20J06; Secondary 16G30, 18E30
- DOI: https://doi.org/10.1090/tran/7297
- MathSciNet review: 3885152
Dedicated: To Dave Benson on the occasion of his 60th birthday