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Dévissages des F-complexes de D-modules arithmétiques en F-isocristaux surconvergents

Daniel Caro
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Abstract

Nous définissons et étudions les dévissages des $F$-complexes de $\mathcal{D}$-modules arithmétiques en $F$-isocristaux surconvergents. Nous prouvons que les $F$-complexes surholonomes sont dévissables en $F$-isocristaux surconvergents. On établit ensuite une formule cohomologique, étendant celle d'Étesse et Le Stum, des fonctions $L$ associées aux duaux des $F$-complexes de $\mathcal{D}$-modules arithmétiques dévissables en $F$-isocristaux surconvergents. Puis, nous obtenons un analogue $p$-adique de Weil II étendant celui de Kedlaya.

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Daniel Caro. 2005-04-12. Dévissages des F-complexes de D-modules arithmétiques en F-isocristaux surconvergents. https://doi.org/10.1007/s00222-006-0517-9

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