Abstract.
Abstract. Let X be a nonsingular projective variety defined over an algebraically closed field k. In the characteristic zero case, the Kawamata-Viehweg vanishing theorem for X is an important tool in the adjunction theory and the minimal model program. On the other hand, in positive characteristic cases, an analog of Kodaira vanishing theorem for X was proved by Raynaud under the condition that X has a lifting over W 2 (k), the ring of Witt vectors of length two. ¶In this paper we prove the Kawamata-Viehweg vanishing theorem for a nonsingular projective surface defined over an algebraically closed field of characteristic p > 0. In particular, we give an explicit condition that the cohomology groups vanish. This is based on Shepherd-Barron's result on the instability of rank 2 locally free sheaves on a surface in positive characteristic.
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Received: 25.6.1997
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Terakawa, H. On the Kawamata-Viehweg vanishing theorem for a surface in positive characteristic. Arch. Math. 71, 370–375 (1998). https://doi.org/10.1007/s000130050279
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DOI: https://doi.org/10.1007/s000130050279