2022/10/04 by Jon Carlson, Carlson, Jon F.
Mathematics · #18G80 #20C20 (primary) #20J06 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2210.01424
openalex publication_date 2022/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose that G is a finite group and k is a field of characteristic p >0. Let M be the thick tensor ideal of finitely generated modules whose support variety is in a fixed subvariety V of the projectivized prime ideal spectrum Proj H^*(G,k). Let C denote the Verdier localization of the stable module category stmod(kG) at M. We show that if V is a finite collection of closed points and if the p-rank every maximal elementary abelian p-subgroups of G is at least 3, then the endomorphism ring of the trivial module in C is a local ring whose unique maximal ideal is infinitely generated and nilpotent. In addition, we show an example where the endomorphism ring in C of a compact object is not finitely presented as a module over the endomorphism ring of the trivial module.