Séminaire de Mathématique

Wild ramification and the cotangent bundle

by Prof. Takeshi SAITO (Tokyo University & IHÉS)

Amphitéâtre Léon Motchane (IHES)

Amphitéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
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.