The coherent cohomology ring of an algebraic group

Abstract

Let $G$ be a group scheme of finite type over a field, and consider the cohomology ring $H^{\ast }(G)$ with coefficients in the structure sheaf. We show that $H^{\ast }(G)$ is a free module of finite rank over its component of degree 0, and is the exterior algebra of its component of degree 1. When $G$ is connected, we determine the Hopf algebra structure of $H^{\ast }(G)$.

minor corrections, final version, to appear at Algebras and Representation Theory

References in corpus (1)

• Homogeneous bundles over abelian varieties