We consider G, a linear algebraic group defined over K, an algebraically closed field (ACF). By considering K as an embedded residue field of an algebraically closed valued field K, we can associate to it a compact G-space K consisting of μ-types on G. We show that for each pμ ∈ SGμ (K), Stabμ (p) = Stab(pμ) is a solvable infinite algebraic group when pμ is centered at infinity and residually algebraic. Moreover, we give a description of the dimension of Stab (pμ) in terms of the dimension of p.
|Journal||Journal of the Institute of Mathematics of Jussieu|
|State||Accepted/In press - 1 Jan 2021|
- Peterzil-Steinhorn subgroups
- affine algebraic groups
- definable Berkovich spaces
ASJC Scopus subject areas
- Mathematics (all)