Le Bois Marie
35, route de Chartres
We define the characteristic cycle of a locally constant étale sheaf on a smooth variety in positive characteristic, ramified along the boundary, as a cycle in the cotangent bundle of the variety, at least on a neighborhood of the generic point of the divisor on the boundary.
We discuss a compatibility with pull-back and local acyclicity in non-characteristic situations. We also give a relation with the characteristic cohomology class and the Euler-Poincaré characteristic.