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Log-isocristaux surconvergents et holonomie

Part of: (Co)homology theory

Published online by Cambridge University Press:  24 September 2009

Daniel Caro
Daniel Caro*
Affiliation:
Laboratoire de MathĂ©matiques Nicolas Oresme, UniversitĂ© de Caen, Campus 2, 14032 Caen Cedex, France (email: [email protected])
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Abstract

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Let đ’± be a complete discrete valuation ring of unequal characteristic with perfect residue field. Let be a separated smooth formal đ’±-scheme, đ’” be a normal crossing divisor of , be the induced formal log-scheme over đ’± and be the canonical morphism. Let X and Z be the special fibers of and đ’”, T be a divisor of X and ℰ be a log-isocrystal on overconvergent along T, that is, a coherent left -module, locally projective of finite type over . We check the relative duality isomorphism: . We prove the isomorphism , which implies their holonomicity as -modules. We obtain the canonical morphism ρℰ : uT,+(ℰ)→ℰ(†Z). When ℰ is moreover an isocrystal on overconvergent along T, we prove that ρℰ is an isomorphism.

Keywords

arithmetical 𝒟-moduleslog-isocrystalsholonomicity

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 145 , Issue 6 , November 2009 , pp. 1465 - 1503
Copyright
Copyright © Foundation Compositio Mathematica 2009

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