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, Tome 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 𝔽p. Notre outil clé est un résultat récent de Cadoret, Hui et Tamagawa.

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Révisé le :
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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
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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, Tome 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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  • Gebhard Böckle; Wojciech Gajda; Sebastian Petersen On the semisimplicity of reductions and adelic openness for E-rational compatible systems over global function fields, Transactions of the American Mathematical Society, Volume 372 (2019) no. 8, pp. 5621-5691 | DOI:10.1090/tran/7788 | Zbl:1471.11176

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