The prime spectra of relative stable module categories

Baland, S., Chirvasitu, A. and Stevenson, G. (2019) The prime spectra of relative stable module categories. Transactions of the American Mathematical Society, 371(1), pp. 489-503. (doi: 10.1090/tran/7297)

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/tn, 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Stevenson, Dr Gregory
• Authors: Baland, S., Chirvasitu, A., and Stevenson, G.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Transactions of the American Mathematical Society
• Publisher: American Mathematical Society
• ISSN: 0002-9947
• ISSN (Online): 1088-6850
• Published Online: 20 July 2018
• Copyright Holders: Copyright © 2017 American Mathematical Society
• First Published: First published in Transactions of the American Mathematical Society 371(1): 489-503
• Publisher Policy: Reproduced in accordance with the publisher copyright policy