On the exponent of geometric unipotent radicals of pseudo-reductive groups

Abstract

Let $k^{\prime }/k$ be a finite purely inseparable field extension and let $G^{\prime }$ be a reductive $k^{\prime }$-group. We denote by $G={\mathbb{R}}_{k^{\prime }/k}(G^{\prime })$ the Weil restriction of $G^{\prime }$ across $k^{\prime }/k$, a pseudo-reductive group. This article gives bounds for the exponent of the geometric unipotent radical $\RR_{u}(G_{\bar{k}})$ in terms of invariants of the extension $k^{\prime }/k$, starting with the case $G'=\GL_n$ and applying these results to the case where $G^{\prime }$ is a simple group.

10 pages; v2 deals with all split simple groups under mild constraints on the characteristic; to appear in Archiv der Mathematik

References in corpus (1)

• The Structure of Root Data and Smooth Regular Embeddings of Reductive Groups