Cohomological finite generation for restricted Lie superalgebras and finite supergroup schemes

Abstract

We prove that the cohomology ring of a finite-dimensional restricted Lie superalgebra over a field of characteristic $p>2$ is a finitely-generated algebra. Our proof makes essential use of the explicit projective resolution of the trivial module constructed by J. Peter May for any graded restricted Lie algebra. We then prove that the cohomological finite generation problem for finite supergroup schemes over fields of odd characteristic reduces to the existence of certain conjectured universal extension classes for the general linear supergroup $GL(m|n)$ that are similar to the universal extension classes for $G{L}_n$ exhibited by Friedlander and Suslin.

32 pages

Cited by in corpus (4)

• Cohomological finite-generation for finite supergroup schemes
• On support varieties for Lie superalgebras and finite supergroup schemes
• Graded analogues of one-parameter subgroups and applications to the cohomology of $G{L}_{m|n(r)}$
• Support varieties and modules of finite projective dimension for modular Lie superalgebras (with an appendix on homological dimensions over Noether Algebras by Luchezar L. Avramov and Srikanth B. Iyengar)