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Fonctions L associées aux $\mathcal{D}$-modules arithmétiques. Cas des courbes

Published online by Cambridge University Press:  13 January 2006

Daniel Caro
Daniel Caro
Affiliation:
NWF I - Mathematik, Universität Regensburg, Universitätsstraße 31, 93053 Regensburg, Germanydaniel.caro@mathematik.uni-regensburg.de Department of Mathematical Sciences, South Road, Durham DH1 3LE, UK
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Abstract

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We prove that holonomic arithmetical ${\mathcal{D}}$-modules over curves have finite fibers. We also define L-functions associated with arithmetical ${\mathcal{D}}$-modules and, when the scheme is a curve, we show a cohomological formula. Furthermore, we prove that F-isocrystals over curves are holonomic.

Keywords

L-functionarithmetical ${\mathcal{D}}$-modulesisocrystalFrobeniusholonomicity14F1014F3014F4013D0713D2513N1032C38
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 1 , January 2006 , pp. 169 - 206
Copyright
Foundation Compositio Mathematica 2006