# A vanishing theorem in characteristic p

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Junecue Suh, IAS
Fine Hall 322

While the classical Kodaira vanishing theorem is false in general in characteristic $p>0$, Deligne, Illusie and Raynaud proved that it remains true under some mild (liftability and dimension) conditions. It has then been generalized in two directions: (1) Esnault and Viehweg allowed the line bundle to be somewhat less than ample and (2) Illusie covered the case with some nontrivial coefficients. We prove a common generalization of the two, which then yields a vanishing theorem of Kollár type.