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Comparison between Swan conductors and characteristic cycles

Part of: (Co)homology theory

Published online by Cambridge University Press:  10 March 2010

Tomoyuki Abe
Tomoyuki Abe*
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguroku, Tokyo, Japan (email: abetomo@ms.u-tokyo.ac.jp)
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Abstract

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In this paper, we define Swan conductors for unit-root overconvergent F-isocrystals using the theory of arithmetic 𝒟-modules due to Berthelot. Our Swan conductors are compared with the Swan conductors for ℓ-adic sheaves constructed by Kato and Saito using a geometric method. As an application, we prove the integrality of Swan conductors in the sense of Kato and Saito under the ‘resolution of singularities’ assumption.

Keywords

arithmetic 𝒟-modulesoverholonomic modulesramification theorySwan conductors

MSC classification

Secondary: 14F20: Étale and other Grothendieck topologies and (co)homologies 14F30: $p$-adic cohomology, crystalline cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 3 , May 2010 , pp. 638 - 682
Copyright
Copyright © Foundation Compositio Mathematica 2010

References

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