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- Title
On localizations of the characteristic classes of ℓ-adic sheaves and conductor formula in characteristic p > 0.
- Authors
Tsushima, Takahiro
- Abstract
Abbes, Kato and Saito generalize the Grothendieck-Ogg-Shafarevich formula to an arbitrary dimension (Kato and Saito in Ann. Math. 168:33-96, 2008; Abbes and Saito in Invent. Math. 168:567-612, 2007). In this paper, assuming the strong resolution of singularities, we prove a localized version of a formula proved using the characteristic class of an ℓ-adic sheaf by Abbes and Saito (Invent Math 168:567-612, 2007). We prove a localized version of the Lefschetz-Verdier trace formula proved in Grothendieck (Formule de Lefschetz, exposé III, SGA 5, Lect. Notes Math., vol 589, pp 372-406, Exp. X, Springer, Berlin, 1977 [Théorème 4.4]). As an application, we prove a conductor formula in an arbitrary dimension in the equal characteristic case.
- Subjects
CHARACTERISTIC classes; DIFFERENTIAL topology; POINCARE series; INVARIANTS (Mathematics); MATHEMATICAL singularities; ALGEBRAIC geometry
- Publication
Mathematische Zeitschrift, 2011, Vol 269, Issue 1/2, p411
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-010-0743-0