Homomorphisms of algebraic groups: representability and rigidity

DOI10.1307/MMJ/20217214arXiv2101.12460MaRDI QIDQ6359348

Michel Brion

Publication date: 29 January 2021

Abstract: Given two algebraic groups $G$, $H$ over a field $k$, we investigate the representability of the functor of morphisms (of schemes) $mathbfHom(G,H)$ and the subfunctor of homomorphisms (of algebraic groups) $mathbf{Hom}_{mgp}(G,H)$. We show that $mathbfHom(G,H)$ is represented by a group scheme, locally of finite type, if the $k$-vector space $mathcalO(G)$ is finite-dimensional; the converse holds if $H$ is not 'etale. When $G$ is linearly reductive and $H$ is smooth, we show that $mathbf{Hom}_{mgp}(G,H)$ is represented by a smooth scheme $M$; moreover, every orbit of $H$ acting by conjugation on $M$ is open.

Mathematics Subject Classification ID

Group schemes (14L15) Schemes and morphisms (14A15)

This page was built for publication: Homomorphisms of algebraic groups: representability and rigidity

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6359348)