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Lectures
Seminar information archive ～04/15｜Next seminar｜Future seminars 04/16～
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)
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.
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.
