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.
@article{PMIHES_2004__100__5_0, author = {Kato, Kazuya and Saito, Takeshi}, title = {On the conductor formula of Bloch}, journal = {Publications Math\'ematiques de l'IH\'ES}, volume = {99}, year = {2004}, pages = {5-151}, doi = {10.1007/s10240-004-0026-6}, mrnumber = {2102698}, zbl = {1099.14009}, language = {en}, url = {http://dml.mathdoc.fr/item/PMIHES_2004__100__5_0} }
Kato, Kazuya; Saito, Takeshi. On the conductor formula of Bloch. Publications Mathématiques de l'IHÉS, Tome 99 (2004) pp. 5-151. doi : 10.1007/s10240-004-0026-6. http://gdmltest.u-ga.fr/item/PMIHES_2004__100__5_0/
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