The twisted forms of a semisimple group over an 𝔽 q -curve
Rony A. Bitan1; Ralf Köhl2; Claudia Schoemann3
1 Afeka, Tel-Aviv Academic College of Engineering Tel-Aviv, Israel Bar-Ilan University Ramat-Gan, Israel
2 JLU Giessen Mathematisches Institut Arndtstr. 2 35392 Giessen, Germany
3 Leibniz University Hannover Institute for Algebraic Geometry Welfengarten 1 30167 Hannover, Germany
Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 1, pp. 17-38.

Let C be a smooth, projective and geometrically connected curve defined over a finite field 𝔽 q . Given a semisimple C-S-group scheme G ̲ where S is a finite set of closed points of C, we describe the set of (𝒪 S -classes of) twisted forms of G ̲ in terms of geometric invariants of its fundamental group F(G ̲).

Soit C une courbe projective, lisse et connexe définie sur un corps fini 𝔽 q . Étant donné un C-S-schéma en groupes semisimples où S est un ensemble fini de points fermés de C, nous décrivons l’ensemble de (𝒪 S -classes de) formes tordues de G ̲ en termes d’invariants géométriques de son groupe fondamental F(G ̲).

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DOI: 10.5802/jtnb.1150
Classification: 11G20, 11G45, 11R29
Keywords: Class number, Hasse principle, Tamagawa number, étale cohomology
Rony A. Bitan 1; Ralf Köhl 2; Claudia Schoemann 3

1 Afeka, Tel-Aviv Academic College of Engineering Tel-Aviv, Israel Bar-Ilan University Ramat-Gan, Israel
2 JLU Giessen Mathematisches Institut Arndtstr. 2 35392 Giessen, Germany
3 Leibniz University Hannover Institute for Algebraic Geometry Welfengarten 1 30167 Hannover, Germany
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Rony A. Bitan; Ralf Köhl; Claudia Schoemann. The twisted forms of a semisimple group over an $\protect \mathbb{F}_q$-curve. Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 1, pp. 17-38. doi : 10.5802/jtnb.1150. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1150/

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