The coherent cohomology ring of an algebraic group

Details The coherent cohomology ring of an algebraic group The coherent cohomology ring of an algebraic group

2012-04-12

arxiv.org/abs/1204.2628v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

Let $G$ be a group scheme of finite type over a field, and consider the
cohomology ring $H^*(G)$ with coefficients in the structure sheaf. We show that
$H^*(G)$ 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 $H^*(G)$.

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