Étale difference algebraic groups
Annales de l'Institut Fourier, Online first, 69 p.

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.

Les groupes algébriques aux différences étales sont des analogues aux différence des groupes algébriques étales. Le résultat principal de cet article est un théorème de décomposition de type Jordan–Hölder pour ces groupes. Nous montrons que tout groupe algébrique aux différences étale peut être construit à partir de groupes algébriques étales simples et de deux groupes algébriques aux différences étales finis. Les groupes algébriques étales simples apparaissant dans cette décomposition satisfont une certaine propriété d’unicité.

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DOI: 10.5802/aif.3621
Classification: 14L15, 12H10, 37B05
Keywords: Difference algebraic group, étale algebraic group, expansive endomorphism, profinite group.
Mot clés : Groupe algébrique aux différences, groupe algébrique étale, endomorphisme expansif, groupe profini.
Wibmer, Michael 1

1 Institute of Analysis and Number Theory Graz University of Technology Kopernikusgasse 24 8010 Graz (Austria)
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Wibmer, Michael. Étale difference algebraic groups. Annales de l'Institut Fourier, Online first, 69 p.

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