A variational open image theorem in positive characteristic

Böckle, Gebhard; Gajda, Wojciech; Petersen, Sebastian

doi:10.5802/jtnb.1059

Böckle, Gebhard ¹ ; Gajda, Wojciech ² ; Petersen, Sebastian 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

Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 965-977.

Résumé
Abstract

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.

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.

Reçu le : 2017-07-04
Révisé le : 2017-07-23
Accepté le : 2017-08-17
Publié le : 2019-03-29

MR Zbl

DOI : 10.5802/jtnb.1059

Classification : 11G10, 14K15
Mots clés : Compatible system, adelic openness, positive characteristic

Affiliations des auteurs :

Böckle, Gebhard ¹ ; Gajda, Wojciech ² ; Petersen, Sebastian ³

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     title = {A variational open image theorem in positive characteristic},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {965--977},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {30},
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Böckle, Gebhard; Gajda, Wojciech; Petersen, Sebastian. A variational open image theorem in positive characteristic. Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 965-977. doi : 10.5802/jtnb.1059. http://archive.numdam.org/articles/10.5802/jtnb.1059/

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