Peterzil-Steinhorn Subgroups and μ-Stabilizers in ACF

Moshe Kamensky; Sergei Starchenko; Jinhe Ye

doi:10.1017/S147474802100030X

Peterzil-Steinhorn Subgroups and μ-Stabilizers in ACF

Moshe Kamensky, Sergei Starchenko, Jinhe Ye

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 SμG(k) consisting of μ-types on G. We show that for each {equation presented}, 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 language	English
Pages (from-to)	1003-1022
Number of pages	20
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	22
Issue number	3
DOIs	https://doi.org/10.1017/S147474802100030X
State	Published - 21 May 2023

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1017/S147474802100030X

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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 SμG(k) consisting of μ-types on G. We show that for each {equation presented}, 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.",

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AU - Starchenko, Sergei

AU - Ye, Jinhe

N1 - Publisher Copyright: © The Author(s), 2021. Published by Cambridge University Press.

PY - 2023/5/21

Y1 - 2023/5/21

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 SμG(k) consisting of μ-types on G. We show that for each {equation presented}, 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 SμG(k) consisting of μ-types on G. We show that for each {equation presented}, 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 - -stabilizers

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KW - definable Berkovich spaces

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Peterzil-Steinhorn Subgroups and μ-Stabilizers in ACF

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Keywords

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