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Displaying similar documents to “Ramification of local fields with imperfect residue fields. II.”

On the conductor formula of Bloch

Kazuya Kato, Takeshi Saito (2004)

Publications Mathématiques de l'IHÉS

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In [6], S. Bloch conjectures a formula for the Artin conductor of the ℓ-adic etale cohomology of a regular model of a variety over a local field and proves it for a curve. The formula, which we call the conductor formula of Bloch, enables us to compute the conductor that measures the wild ramification by using the sheaf of differential 1-forms. In this paper, we prove the formula in arbitrary dimension under the assumption that the reduced closed fiber has normal crossings.

Almost étale extensions of Fontaine rings and log-crystalline cohomology in the semi-stable reduction case

Rémi Shankar Lodh (2011)

Annales de l’institut Fourier

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Let K be a field of characteristic zero complete for a discrete valuation, with perfect residue field of characteristic p > 0 , and let K + be the valuation ring of K . We relate the log-crystalline cohomology of the special fibre of certain affine K + -schemes X = Spec ( R ) with good or semi-stable reduction to the Galois cohomology of the fundamental group π 1 ( X K ¯ ) of the geometric generic fibre with coefficients in a Fontaine ring constructed from R . This is based on Faltings’ theory of almost étale extensions. ...