2012 / June Volume 7 No.2
Endotrivial Modules For Finite Group Schemes II
| Published Date |
2012 / June
|
|---|---|
| Title | Endotrivial Modules For Finite Group Schemes II |
| Author | |
| Keyword | |
| Download | |
| Pagination | 271-289 |
| Abstract | It is well known
that if $G$ is a finite group then the group of endotrivial modules
is finitely generated. In this paper we prove that for an arbitrary
finite group scheme $G$, and for any fixed integer $n > 0$, there
are only finitely many isomorphism classes of endotrivial modules of
dimension $n$. This provides evidence to support the speculation
that the group of endotrivial modules for a finite group scheme is
always finitely generated. The result also has some applications to
questions about lifting and twisting the structure of endotrivial
modules in the case that $G$ is an infinitesimal group scheme
associated to an algebraic group.
|
| AMS Subject Classification |
20C20
|
| Received |
2011-06-26
|
| Accepted |
2011-06-30
|