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On nearby cycles and 𝒟-modules of log schemes in characteristic p>0

Part of: (Co)homology theory

Published online by Cambridge University Press:  16 June 2010

Takeshi Tsuji
Takeshi Tsuji*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro, Tokyo 153-8914, Japan (email: t-tsuji@ms.u-tokyo.ac.jp)
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Abstract

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Let K be a complete discrete valuation field of mixed characteristic (0,p) with a perfect residue field k. For a semi-stable scheme over the ring of integers OK of K or, more generally, for a log smooth scheme of semi-stable type over k, we define nearby cycles as a single 𝒟-module endowed with a monodromy ∂logt, whose cohomology should give the log crystalline cohomology. We also explicitly describe the monodromy filtration of the 𝒟-module with respect to the endomorphism ∂logt, and construct a weight spectral sequence for the cohomology of the nearby cycles.

Keywords

nearby cycles𝒟-modulelogarithmic scheme

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 146 , Issue 6 , November 2010 , pp. 1552 - 1616
Copyright
Copyright © Foundation Compositio Mathematica 2010

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