On Unipotent Radicals of Pseudo-Reductive Groups

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Date
2017-04-27MFO Scientific Program
Research in Pairs 2015Series
Oberwolfach Preprints;2017,12Author
Bate, Michael
Martin, Benjamin
Röhrle, Gerhard
Stewart, David I.
Metadata
Show full item recordOWP-2017-12
Abstract
We establish some results on the structure of the geometric unipotent
radicals of pseudo-reductive k-groups. In particular, let $k'$ be a purely
inseparable field extension of k of degree $p^e$ and let $G$ denote the Weil
restriction of scalars $\mathrm{R}_{k'/k}(G')$ of a reductive $k'$-group $G'$. We prove that
the unipotent radical $\mathscr{R}_u(G_{\bar k})$ of the extension of scalars of $G$ to the
algebraic closure $\bar k$ of $k$ has exponent $e$. Our main theorem is to give
bounds on the nilpotency class of geometric unipotent radicals of standard
pseudo-reductive groups, which are sharp in many cases.