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Arithmetic 𝒟-modules on the unit disk. With an appendix by Shigeki Matsuda

Part of: (Co)homology theory

Published online by Cambridge University Press:  09 November 2011

Richard Crew
Richard Crew*
Affiliation:
Department of Mathematics, The University of Florida, Gainesville, FL 32601, USA (email: rcrew@ufl.edu)
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Abstract

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Let 𝒱 be a complete discrete valuation ring of mixed characteristic. We classify arithmetic 𝒟-modules on Spf(𝒱[[t]]) up to certain kind of ‘analytic isomorphism’. This result is used to construct canonical extensions (in the sense of Katz and Gabber) for objects of this category.

Keywords

arithmetic 𝒟-modulecanonical extension

MSC classification

Secondary: 14F30: $p$-adic cohomology, crystalline cohomology 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 1 , January 2012 , pp. 227 - 268
Copyright
Copyright © Foundation Compositio Mathematica 2011

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