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

Publisher： Cambridge University Press

E-ISSN： 1570-5846|148|1|227-268

ISSN： 0010-437x

Source： Compositio Mathematica, Vol.148, Iss.1, 2012-01, pp. : 227-268

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Abstract

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.

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