Connections between group representations and cohomology (Q2759658)

Over the past thirty years, module theory for finite groups over a field of prime characteristic has developed significantly through the study of cohomology of groups and the use of geometry. This article is an excellent survey of these developments with numerous nice examples. In particular, the article discusses rank varieties (which are defined purely module theoretically), cohomological support varieties (which are defined in terms of cohomology), the significance of these varieties, and the relationship between them. Further discussion is given of the key role played by the elementary Abelian subgroups of a given group. Finally, there is a discussion of more recent work in which the definitions of these varieties (originally given for finite dimensional modules) have been extended to arbitrary modules.NEWLINENEWLINENEWLINEI highly recommend this article as a starting point for anyone wishing to learn more about cohomological varieties for finite groups and the deep connections between cohomology and representations. The references provide a thorough list of original sources for the interested reader to pursue.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00049].