Nearby cycles over general bases and duality

Nearby cycles over general bases and duality

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Weizhe Zheng, Morningside Center of Mathematics (Chinese Academy of Sciences)
Fine Hall 214

Over one-dimensional bases, Gabber and Beilinson proved theorems on the commutation of the nearby cycle functor and the vanishing cycle functor with duality. In this talk, I will explain a way to unify the two theorems, confirming a prediction of Deligne. I will also discuss the case of higher-dimensional bases and applications to local acyclicity, following suggestions of Illusie and Gabber. This is joint work with Qing Lu.