Nearby cycles over general bases and duality

Weizhe Zheng
Chinese Academy of Sciences and Princeton University
Thursday, March 14, 2019 - 1:25pm to 2:25pm
Vincent Hall 113

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.