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

  • Takeshi Tsuji (a1)

Abstract

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.

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References

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

  • Takeshi Tsuji (a1)

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