Finiteness theorems for algebraic tori over function fields

Andrei S. Rapinchuk; Igor A. Rapinchuk

doi:10.5802/crmath.248

Géométrie algébrique, Théorie des nombres

Finiteness theorems for algebraic tori over function fields

Andrei S. Rapinchuk ¹ ; Igor A. Rapinchuk ²

¹ Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA
² Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 939-944.

Résumé
Abstract

Nous présentons plusieurs résultats de finitude pour les tores (et, plus généralement, pour les groupes algébriques dont la composante connexe est un tore) définis sur les corps de type fini et les corps de fonctions des variétés algébriques définies sur les corps satisfaisant la condition (F) de Serre.

We present a number of finiteness results for algebraic tori (and, more generally, for algebraic groups with toric connected component) over two classes of fields: finitely generated fields and function fields of algebraic varieties over fields of type (F), as defined by J.-P. Serre.

Reçu le : 2021-03-09
Accepté le : 2021-07-23
Accepté après révision le : 2021-07-31
Publié le : 2021-10-06

DOI : 10.5802/crmath.248

Affiliations des auteurs :

Andrei S. Rapinchuk ¹ ; Igor A. Rapinchuk ²

¹ Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA
² Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Andrei S. Rapinchuk and Igor A. Rapinchuk},
     title = {Finiteness theorems for algebraic tori over function fields},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {939--944},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {8},
     year = {2021},
     doi = {10.5802/crmath.248},
     language = {en},
}

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Andrei S. Rapinchuk; Igor A. Rapinchuk. Finiteness theorems for algebraic tori over function fields. Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 939-944. doi : 10.5802/crmath.248. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.248/

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