Peterzil-Steinhorn Subgroups and μ-Stabilizers in ACF

Moshe Kamensky, Sergei Starchenko, Jinhe Ye

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish
JournalJournal of the Institute of Mathematics of Jussieu
DOIs
StateAccepted/In press - 1 Jan 2021

Keywords

  • Peterzil-Steinhorn subgroups
  • affine algebraic groups
  • definable Berkovich spaces
  • μ-stabilizers

ASJC Scopus subject areas

  • Mathematics (all)

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