Séminaire de Mathématique

# Wild ramification and the cotangent bundle

## by Prof. Takeshi SAITO (Tokyo University & IHÉS)

Europe/Paris
Amphitéâtre Léon Motchane (IHES)

### Amphitéâtre Léon Motchane

#### IHES

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