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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