Vanishing theorems of Kodaira type for Witt canonical sheaves

Abstract

Given a smooth projective variety over a perfect field of positive characteristic, we prove that the higher cohomologies vanish for the tensor product of the Witt canonical sheaf and the Teichmuller lift of an ample invertible sheaf. We also give a generalisation of this vanishing theorem to one of Kawamata-Viehweg type.

arXiv comment51 pages, v3: I made many changes. The proof of Theorem 1.1 has been simplified. The statement of Theorem 1.3 is slightly changed and its proof has been corrected. v4: Minor revisions v5: Minor revisions