2015/09/09 by Jon F. Carlson, Jon Carlson, Sunil K. Chebolu +5
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1509.02845
Final version, 11 pages, to appear in Canadian Mathematical Bulletin
openalex publication_date 2015/09/09 · arxiv created 2016/06/13 · arxiv updated 2016/06/14 · 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. 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 showed that the thick subcategory generated by the trivial module has 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 some variations of ghosts maps. In particular, we consider the behavior of ghost maps under restriction and induction functors. We find all groups satisfying a strong form of Freyd's generating hypothesis and show that ghost can be detected on a finite range of Tate cohomology. We also consider maps which mimic ghosts in high degrees.