Geodesic
Overholonomicity of overconvergent $F$-isocrystals over smooth varieties
Daniel Caro1 ; Nobuo Tsuzuki2
1 Laboratoire de Mathématiques Nicolas Oresme<br/>Université de Caen<br/> Campus 2<br/> 14032 Caen cedex<br/> France
2 Mathematical Institute<br/> Tohoku University<br/> Sendai 980-8576<br/> Japan
Annals of mathematics, Tome 176 (2012) no. 2, pp. 747-813.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove the overholonomicity of overconvergent $F$-isocrystals over
smooth varieties. This implies that the notions of overholonomicity and devissability in overconvergent $F$-isocrystals are equivalent. Then the overholonomicity is stable under tensor products. So, the overholonomicity gives a $p$-adic cohomology stable under Grothendieck’s cohomological operations.
DOI : 10.4007/annals.2012.176.2.2

Daniel Caro 1 ; Nobuo Tsuzuki 2

1 Laboratoire de Mathématiques Nicolas Oresme<br/>Université de Caen<br/> Campus 2<br/> 14032 Caen cedex<br/> France
2 Mathematical Institute<br/> Tohoku University<br/> Sendai 980-8576<br/> Japan 
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Daniel Caro; Nobuo Tsuzuki. Overholonomicity of overconvergent  $F$-isocrystals over smooth varieties. Annals of mathematics, Tome 176 (2012) no. 2, pp. 747-813. doi : 10.4007/annals.2012.176.2.2. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.2.2/

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