Mathematical Research Letters

Volume 17 (2010)

Number 3

Strongly liftable schemes and the Kawamata-Viehweg vanishing in positive characteristic

Pages: 563 – 572

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n3.a13

Author

Qihong Xie (Fudan University)

Abstract

A smooth scheme $X$ over a field $k$ of positive characteristic is said to be strongly liftable, if $X$ and all prime divisors on $X$ can be lifted simultaneously over $W_2(k)$. In this paper, we give some concrete examples and properties of strongly liftable schemes. As an application, we prove that the Kawamata-Viehweg vanishing theorem in positive characteristic holds on any normal projective surface which is birational to a strongly liftable surface.

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