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On the conductor formula of Bloch


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.

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Correspondence to Kazuya Kato or Takeshi Saito.

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Kato, K., Saito, T. On the conductor formula of Bloch. Publ. Math., Inst. Hautes Étud. Sci. 100, 5–151 (2004).

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  • Spectral Sequence
  • Cartier Divisor
  • Distinguished Triangle
  • Noetherian Scheme
  • Simple Normal Crossing