| In characteristic zero birational algebraic geometry, Kawamata-Viehweg vanishing is a centrally important tool. For some applications in characteristic p > 0, one may use Frobenius and perturbations as a replacement for resolution of singularities and Kawamata-Viehweg vanishing. This talk will show how to use Bhatt's vanishing theorem for absolute integral closures mixed characteristic as a replacement for resolutions and Kawamata-Viehweg vanishing theorems in a number of applications. This is joint work with B. Bhatt, L. Ma, Z. Patakfalvi, K. Tucker, J. Waldron and J. Witaszek. |