Étale difference algebraic groups

Michael Wibmer

doi:10.5802/aif.3621

Étale difference algebraic groups

Michael Wibmer^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

Étale difference algebraic groups are a difference analog of étale algebraic groups. Our main result is a Jordan–Hölder type decomposition theorem for these groups. Roughly speaking, it shows that any étale difference algebraic group can be build up from simple étale algebraic groups and two finite étale difference algebraic groups. The simple étale algebraic groups occurring in this decomposition satisfy a certain uniqueness property.

Original language	English
Pages (from-to)	1451-1519
Number of pages	69
Journal	Annales de l'Institut Fourier
Volume	74
Issue number	4
DOIs	https://doi.org/10.5802/aif.3621
Publication status	Published - 2024

Keywords

Difference algebraic group
expansive endomorphism
profinite group
étale algebraic group

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.5802/aif.3621Licence: CC BY-ND 4.0

Cite this

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title = "{\'E}tale difference algebraic groups",

abstract = "{\'E}tale difference algebraic groups are a difference analog of {\'e}tale algebraic groups. Our main result is a Jordan–H{\"o}lder type decomposition theorem for these groups. Roughly speaking, it shows that any {\'e}tale difference algebraic group can be build up from simple {\'e}tale algebraic groups and two finite {\'e}tale difference algebraic groups. The simple {\'e}tale algebraic groups occurring in this decomposition satisfy a certain uniqueness property.",

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AB - Étale difference algebraic groups are a difference analog of étale algebraic groups. Our main result is a Jordan–Hölder type decomposition theorem for these groups. Roughly speaking, it shows that any étale difference algebraic group can be build up from simple étale algebraic groups and two finite étale difference algebraic groups. The simple étale algebraic groups occurring in this decomposition satisfy a certain uniqueness property.

KW - Difference algebraic group

KW - expansive endomorphism

KW - profinite group

KW - étale algebraic group

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M3 - Article

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Étale difference algebraic groups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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