Student AG Seminar: Flops, derived categories, and liftability of threefolds

Using mixed characteristic minimal model program for fourfolds (under an assumption on mixed characteristic resolution of singularities), Hacon and Witaszek proved that liftability of Calabi-Yau threefolds in positive characteristic is preserved under birational equivalence. In this talk, I will explain the joint work in progress with Perry where we unconditionally prove this result by extending Bridgeland’s work on threefolds flops. This celebrated work of Bridgeland describes threefold flops over the complex numbers as moduli spaces of certain complexes of sheaves, and our work generalizes this description to a relative setting.