**Marco Antei**

University of Lille, France

January 21, 2010

**Galois closure of essentially finite morphisms**:
Let X be a scheme over a field k and f:Y-->X an essentially finite morphism. We construct a "Galois closure" of f, i.e. the smallest possible torsor dominating it. As an application we construct the Galois closure of towers of torsors. (Work in collaboration with Michel
Emsalem).