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Archiv der Mathematik

, Volume 71, Issue 5, pp 370–375 | Cite as

On the Kawamata-Viehweg vanishing theorem for a surface in positive characteristic

  • Hiroyuki Terakawa
Article

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 W2 (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.

Keywords

Model Program Minimal Model Cohomology Group Positive Characteristic Projective Variety 

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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Hiroyuki Terakawa
    • 1
  1. 1.Department of Mathematics School of Education, Waseda University 1-6-1 Nishi-Waseda, Shinjuku-Ku, Tokyo 169-50, JapanJapan

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