2013/01/05 by Qihong Xie, Jian Wu, Xie, Qihong +1 · 1 citation
Computer Science · Mathematics · #14E30 #14F17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14E30 #msc:14F17
paper · pdf · doi:10.48550/arxiv.1301.0857
13 pages
openalex publication_date 2013/01/05 · arxiv created 2013/08/01 · arxiv updated 2013/08/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A smooth scheme X over a field k of positive characteristic is said to be strongly liftable over W2(k), if X and all prime divisors on X can be lifted simultaneously over W2(k). In this paper, we first deduce the Kummer covering trick over W2(k), which can be used to construct a large class of smooth projective varieties liftable over W2(k), and to give a direct proof of the Kawamata-Viehweg vanishing theorem on strongly liftable schemes. Secondly, we generalize almost all of the results in [Xie10, Xie11] to the case where everything is considered over W(k), the ring of Witt vectors of k.