Ghosts and Strong Ghosts in the Stable Category. Issue 4 (1st December 2016)
- Record Type:
- Journal Article
- Title:
- Ghosts and Strong Ghosts in the Stable Category. Issue 4 (1st December 2016)
- Main Title:
- Ghosts and Strong Ghosts in the Stable Category
- Authors:
- Carlson, Jon F.
Chebolu, Sunil K.
Mináč, Ján - Abstract:
- Abstract: 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 variations of ghost 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 ghosts can be detected on a finite range of degrees of Tate cohomology. We also consider maps that mimic ghosts in high degrees.
- Is Part Of:
- Canadian mathematical bulletin =. Volume 59:Issue 4(2016)
- Journal:
- Canadian mathematical bulletin =
- Issue:
- Volume 59:Issue 4(2016)
- Issue Display:
- Volume 59, Issue 4 (2016)
- Year:
- 2016
- Volume:
- 59
- Issue:
- 4
- Issue Sort Value:
- 2016-0059-0004-0000
- Page Start:
- 682
- Page End:
- 692
- Publication Date:
- 2016-12-01
- Subjects:
- 20C20 -- 20J06 -- 55P42
Tate cohomology -- ghost maps -- stable module category -- almost split sequence -- periodic cohomology
Mathematics -- Periodicals
Mathematics
Periodicals
510.5 - Journal URLs:
- http://www.cms.math.ca/cmb/ ↗
https://www.cambridge.org/core/journals/canadian-mathematical-bulletin ↗ - DOI:
- 10.4153/CMB-2016-038-4 ↗
- Languages:
- English
- ISSNs:
- 0008-4395
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD Digital store
- Ingest File:
- 24164.xml