Endotrivial Modules For Finite Group Schemes II
by
Jon F. Carlson
Daniel K. Nakano
Vol. 7 No. 2 (2012) P.271~P.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.
KEYWORDS
Cohomology, endotrivial modules, lifting module structures
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20C20
MILESTONES
Received: 2011-04-02
Revised : 2011-06-26
Accepted: 2011-06-30
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