On the topology of geometric and rational orbits for algebraic group actions over valued fields
type: Item
instance of: scholarly article
title: On the topology of geometric and rational orbits for algebraic group actions over valued fields
zbMATH Open document ID: 1471.14095
author: Phuong Bac Dao
published in: Journal of Group Theory
publication date: 2020-11-02T00:00:00Z
review text: This paper studies orbits of algebraic groups on affine spaces defined over valued fields, aiming to give relations between closedness of these orbits in the two topologies available in this setting. More precisely, the aim is to relate: (1) Zariski-closedness of an orbit \(G\cdot v\); with (2) closedness of the relative orbit \(G(k)\cdot v\) under the topology induced by the valued field \(k\). The paper gives an overview of what is known about the relationship between these two notions of closedness (for example 2 implies 1 if the field is perfect; 1 implies 2 if the stabilizer is \(k\)-defined), and examples to show the failure of the implications in general. It is shown that 1 and 2 are equivalent if the group \(G\) acting is commutative.
reviewed by: Michael Bate
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 7268924
zbMATH Keywords: actions of algebraic groups
zbMATH Keywords: Zariski closed orbit
zbMATH Keywords: relative closed orbit
zbMATH Keywords: valued fields
MaRDI profile type: Publication
full work available at URL: jgth-2019-0123
OpenAlex ID: W3034422034
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DOI: 10.1515/JGTH-2019-0123
description: scientific article