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Stabilité de l’holonomie sur les variétés quasi-projectives

Part of: (Co)homology theory

Published online by Cambridge University Press:  24 August 2011

Daniel Caro
Daniel Caro*
Affiliation:
Laboratoire de Mathématiques Nicolas Oresme, Université de Caen Campus 2, 14032 Caen Cedex, France (email: daniel.caro@math.unicaen.fr)
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Abstract

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Let 𝒱 be a mixed characteristic complete discrete valuation ring with perfect residue field k. We solve Berthelot’s conjectures on the stability of the holonomicity over smooth projective formal 𝒱-schemes. Then we build a category of F-complexes of arithmetic 𝒟-modules over quasi-projective k-varieties with bounded and holonomic cohomology. We obtain its stability under Grothendieck’s six operations.

Keywords

p-adic cohomologiesarithmetic 𝒟-modulesholonomicityoverconvergent isocrystalsstability

MSC classification

Secondary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14F30: $p$-adic cohomology, crystalline cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 6 , November 2011 , pp. 1772 - 1792
Copyright
Copyright © Foundation Compositio Mathematica 2011

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