Ghosts and Strong Ghosts in the Stable Category
Printed: Dec 2016
Jon F. Carlson,
Sunil K. Chebolu,
Suppose that $G$ is a finite group and $k$ is a field of characteristic
$p\gt 0$. 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
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
In particular, we consider the behavior of ghost maps under
and induction functors. We find all groups satisfying a strong
of Freyd's generating hypothesis and show that ghosts can
be detected on a finite range of degrees of Tate cohomology.
consider maps which mimic ghosts in high degrees.
Tate cohomology, ghost maps, stable module category, almost split sequence, periodic cohomology
20C20 - Modular representations and characters
20J06 - Cohomology of groups
55P42 - Stable homotopy theory, spectra