Mathematical Research Letters
Volume 17 (2010)
Strongly liftable schemes and the Kawamata-Viehweg vanishing in positive characteristic
Pages: 563 – 572
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.