Ghosts and Strong Ghosts in the Stable Category

Canadian mathematical bulletin

Ján Mináč²  Jon F. Carlson³  Sunil K. Chebolu¹ 

[1] Department of Mathematics, Illinois State University, Normal, IL 61790 USA;Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada;Department of Mathematics, University of Georgia, Athens, GA 30602, USA

关键词: Tate cohomology;    ghost maps;    stable module category;    almost split sequence;    periodic cohomology;   

DOI  :  10.4153/CMB-2016-038-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Suppose that $G$ is a finite group and $k$ is a field of characteristic $pgt 0$. A ghost map is a map in the stable category of finitely generated $kG$-modules which induces the zero map in Tate cohomology in all degrees. In an earlier paper we showedthat the thick subcategory generated by the trivial modulehas no nonzero ghost maps if and only if the Sylow $p$-subgroup of $G$ is cyclic of order 2 or 3. In this paper we introduce and study variations of ghostmaps. In particular, we consider the behavior of ghost maps underrestriction and induction functors. We find all groups satisfying a strongform of Freyd's generating hypothesis and show that ghosts can be detected on a finite range of degrees of Tate cohomology.We also consider maps which mimic ghosts in high degrees.

【 授权许可】

Unknown