Quasi-canonical lifting of projective varieties in positive characteristic

TL;DR

This paper introduces new classes of smooth projective varieties in positive characteristic that can be lifted over Witt vectors with additional structures, extending classical results on canonical liftings.

Contribution

It provides a refined criterion for Frobenius liftability and demonstrates algebraization of specific $p$-adic formal schemes, advancing understanding of liftings in positive characteristic.

Findings

New classes of Frobenius liftable varieties identified

Refined form of Mehta-Srinivas classical result established

Algebraization of certain $p$-adic formal schemes proven

Abstract

The main aim of this article is to give new classes of smooth projective varieties over characteristic $p>0$ that admit flat liftings over the Witt vectors together with additional data (logarithmic structure and the Frobenius morphism) by showing a descending property of such Frobenius liftability. We establish a refined form of the classical result due to Mehta-Srinivas on the existence of canonical liftings. For this purpose, we also establish a result on the algebraization of certain $p$-adic formal schemes.