Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic

TL;DR

This paper explores the concept of strongly liftable schemes in positive characteristic, providing examples and properties, and demonstrates that the Kawamata-Viehweg vanishing theorem applies to certain surfaces related to these schemes.

Contribution

It introduces the notion of strongly liftable schemes, offers concrete examples and properties, and applies these to prove a vanishing theorem in positive characteristic.

Findings

Strongly liftable schemes can be explicitly constructed.

Kawamata-Viehweg vanishing holds on surfaces birational to strongly liftable ones.

The paper establishes conditions under which vanishing theorems are valid in positive characteristic.

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.