Algebraic geometry, Number theory
Finiteness theorems for algebraic tori over function fields
Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 939-944.

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.

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.

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DOI: 10.5802/crmath.248
Rapinchuk, Andrei S. 1; Rapinchuk, Igor A. 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
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Rapinchuk, Andrei S.; Rapinchuk, Igor A. Finiteness theorems for algebraic tori over function fields. Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 939-944. doi : 10.5802/crmath.248. http://www.numdam.org/articles/10.5802/crmath.248/

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