Title: Spectra of tensor triangulated categories over category algebras

Author: Fei Xu

Address: Department of Mathematics, Shantou University, 243 University Road, Shantou, Guangdong 515063, China.

email: fxu@stu.edu.cn

Abstract: Let $\C$ be a finite EI category and $k$ a field. We consider the category algebra $k\C$. Suppose $\K(\C)=\D^b(k\C\mbox{-}\mod)$ is the bounded derived category of finitely 
generated left modules. It is a tensor triangulated category and we compute its spectrum in the sense of Balmer. When $\C=G\propto\P$ is a finite transporter category, the category algebra 
becomes Gorenstein so we can define the stable module category $\CM k(G\propto\P)$, of maximal Cohen-Macaulay modules, as a quotient category of $\K(G\propto\P)$. Since $\CM k(G\propto\P)$ 
is also tensor triangulated, we compute its spectrum as well.

These spectra are used to classify tensor ideal thick subcategories of corresponding tensor triangulated categories.