*Séminaire de Géométrie Algébrique de Rennes - Exposé du 4 décembre 2003*

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**Richard CREW** (University of Florida)

**Titre** : Vanishing cycles in rigid cohomology

**Résumé** :

The theory of vanishing cycles is an important tool in the cohomological study of algebraic varieties, but as yet there is no such theory in rigid cohomology. In this talk I will explain one can, in certain situations where the geometry is particularly simple, construct an analogue of the spectral sequence of vanishing cycles. If time permits, I will try to discuss a conjectural construction that works in general.

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