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.


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org: Barbara Bolognese