## Lectures

### 2018/03/09

13:30-14:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Luc Illusie
Sliced nearby cycles and duality, after W. Zheng (ENGLISH)
[ Abstract ]
In the early 1980's Gabber proved duality for nearby cycles and, by a different method, Beilinson proved duality for vanishing cycles in the strictly local case (up to a twist of the inertia action on the tame part). Recently W. Zheng found a simple proof of a result, conjectured by Deligne, which implies them both, and extended it over finite dimensional excellent bases. I will explain the main ideas of his work, which relies on new developments, due to him, of Deligne's theory of fibered and oriented products.