2011/04/01 by Jon F. Carlson, Jon Carlson, Carlson, Jon F. +2
Mathematics · #20C20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20C20
paper · pdf · doi:10.48550/arxiv.1104.0226
arxiv created 2011/04/01 · openalex publication_date 2011/04/01 · arxiv updated 2011/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.