2012 / June Volume 7 No.2
Endotrivial Modules For Finite Group Schemes II
Published Date |
2012 / June
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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.
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AMS Subject Classification |
20C20
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Received |
2011-06-26
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Accepted |
2011-06-30
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