Vanishing theorems via p-adic Hodge theory -- Bhargav Bhatt, Aug 19, 2020.

Abstract: I'll explain an approach to some classical vanishing theorems in algebraic geometry that comes out of p-adic Hodge theory. The primary aim of the talk is to explain why p-adic geometry provides a direct connection between topological objects (e.g., the IC complex) and coherent sheaves (e.g., the canonical bundle). Joint work in progress with Jacob Lurie.