A variational open image theorem in positive characteristic
Gebhard Böckle1; Wojciech Gajda2; Sebastian Petersen3
1 Computational Arithmetic Geometry IWR (Interdisciplinary Center for Scientific Computing) University of Heidelberg Im Neuenheimer Feld 368 69120 Heidelberg, Germany
2 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61614 Poznań, Poland
3 Universität Kassel Fachbereich 10 Wilhelmshöher Allee 73 34121 Kassel, Germany
Journal de Théorie des Nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 965-977.

We prove a variational open adelic image theorem for the Galois action on the cohomology of smooth proper S-schemes where S is a smooth variety over a finitely generated field of positive characteristic. A central tool is a recent result of Cadoret, Hui and Tamagawa.

Nous démontrons un théorème de l’image adélique ouverte variationnel pour l’action du groupe de Galois sur la cohomologie d’un S-schéma propre et lisse, où S est une variété lisse sur un corps de type fini sur 𝔽 p . Notre outil clé est un résultat récent de Cadoret, Hui et Tamagawa.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1059
Classification: 11G10,  14K15
Keywords: Compatible system, adelic openness, positive characteristic
Gebhard Böckle 1; Wojciech Gajda 2; Sebastian Petersen 3

1 Computational Arithmetic Geometry IWR (Interdisciplinary Center for Scientific Computing) University of Heidelberg Im Neuenheimer Feld 368 69120 Heidelberg, Germany
2 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61614 Poznań, Poland
3 Universität Kassel Fachbereich 10 Wilhelmshöher Allee 73 34121 Kassel, Germany 
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Gebhard Böckle; Wojciech Gajda; Sebastian Petersen. A variational open image theorem in positive characteristic. Journal de Théorie des Nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 965-977. doi : 10.5802/jtnb.1059. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1059/

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