Skip to main content

First cohomology of Frobenius kernels and truncated invariants

Posted in
Speaker: 
Rudolf Tange
Affiliation: 
University of Leeds
Date: 
Fri, 2018-11-23 10:30 - 11:30
Location: 
MPIM Lecture Hall

$k$ be an algebraically closed field of characteristic $p > 0$ and let $G$ be a connected reductive group over $k$ with Lie algebra ${g}$. Consider the rings $k[G]$ and $k[{g}]$ of regular functions on $G$ and ${g}$ as $G$-modules via the conjugation action. They have been studied extensively, for example in Kostant’s 1963 paper. I will discuss the result that, under some mild assumptions, the first restricted cohomology of these modules is zero. After this I will discuss the problem of describing the invariants in a certain finite dimensional quotient of $k[{g}]$.

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A