On the conductor formula of Bloch

Kato, Kazuya; Saito, Takeshi

Publications Mathématiques de l'IHÉS, Tome 100 (2004), pp. 5-151.

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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