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D\'evissages des F-complexes de D-modules arithm\'etiques en F-isocristaux surconvergents

Daniel Caro
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Abstract

Nous d\'efinissons et \'etudions les d\'evissages des $F$-complexes de $\mathcal{D}$-modules arithm\'etiques en $F$-isocristaux surconvergents. Nous prouvons que les $F$-complexes surholonomes sont d\'evissables en $F$-isocristaux surconvergents. On \'etablit ensuite une formule cohomologique, \'etendant celle d'\'Etesse et Le Stum, des fonctions $L$ associ\'ees aux duaux des $F$-complexes de $\mathcal{D}$-modules arithm\'etiques d\'evissables en $F$-isocristaux surconvergents. Puis, nous obtenons un analogue $p$-adique de Weil II \'etendant celui de Kedlaya.

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Daniel Caro. 2005-03-28. D\'evissages des F-complexes de D-modules arithm\'etiques en F-isocristaux surconvergents. https://doi.org/10.1007/s00222-006-0517-9

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