TY - JOUR
T1 - Peterzil-Steinhorn Subgroups and μ-Stabilizers in ACF
AU - Kamensky, Moshe
AU - Starchenko, Sergei
AU - Ye, Jinhe
N1 - Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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.
AB - 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.
KW - Peterzil-Steinhorn subgroups
KW - affine algebraic groups
KW - definable Berkovich spaces
KW - μ-stabilizers
UR - http://www.scopus.com/inward/record.url?scp=85111073357&partnerID=8YFLogxK
U2 - 10.1017/S147474802100030X
DO - 10.1017/S147474802100030X
M3 - Article
AN - SCOPUS:85111073357
JO - Journal of the Institute of Mathematics of Jussieu
JF - Journal of the Institute of Mathematics of Jussieu
SN - 1474-7480
ER -