  The Grothendieck-Ogg-Shafarevich formula calculates the l-adic Euler-Poincare
number of an l-adic sheaf on a curve by an invariant produced by the wild
ramification of the l-adic sheaf named Swan class. A. Abbes, K. Kato and T.
Saito generalize this formula to any dimensional scheme. In this paper,
assuming the strong resolution of singularities we prove a localized version of
a formula proved by A. Abbes and T. Saito using the characteristic class of an
l-adic sheaf. As an application, we prove a conductor formula in equal
characteristic.
