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Vanishing theorems of Kodaira type for Witt canonical sheaves

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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 Teichmüller lift of an ample invertible sheaf. We also give a generalisation of this vanishing theorem to one of Kawamata–Viehweg type.

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Acknowledgements

The author would like to thank Piotr Achinger, Yoshinori Gongyo, Luc Illusie, Yujiro Kawamata, Yukiyoshi Nakkajima, and Shuji Saito for useful comments and pointing out mistakes. The author also would like to thank the referee for reading the manuscript carefully and suggesting several improvements. The author was funded by EPSRC and the Grant-in-Aid for Scientific Research (KAKENHI No. 18K13386).

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  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Hiromu Tanaka

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  1. Hiromu Tanaka
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Correspondence to Hiromu Tanaka.

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Tanaka, H. Vanishing theorems of Kodaira type for Witt canonical sheaves. Sel. Math. New Ser. 28, 12 (2022). https://doi.org/10.1007/s00029-021-00736-0

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