Cohomology of finite graded group varieties

TL;DR

This paper proves that the cohomology of certain finite graded Hopf algebras is finitely generated, unifying several classical results in the field.

Contribution

It establishes the finite generation of cohomology for positively graded, local, finite Hopf algebras, introducing conormal elementary quotients as a key tool.

Findings

Cohomology of the specified Hopf algebras is finitely generated.

Unified classical results of Wilkerson, Hopkins-Smith, and Friedlander-Suslin.

Introduced conormal elementary quotients to prove finite generation.

Abstract

We prove that, if $A$ is a positively graded, graded commutative, local, finite Hopf algebra, its cohomology is finitely generated, thus unifying classical results of Wilkerson and Hopkins-Smith, and of Friedlander-Suslin. We do this by showing the existence of conormal elementary quotients.