Global Frobenius Liftability II: Surfaces and Fano Threefolds

TL;DR

This paper advances the theory of Frobenius liftings modulo p^2, focusing on surfaces and Fano threefolds, and confirms a conjecture about their Frobenius liftability.

Contribution

It characterizes Frobenius liftable surfaces and Fano threefolds, extending the previous work and confirming a key conjecture in the field.

Findings

Characterization of Frobenius liftable surfaces.

Confirmation of Frobenius liftability for Fano threefolds.

Development of criteria for compatibility with Frobenius liftings.

Abstract

In this article, a sequel to "Global Frobenius Liftability I" (math:1708:03777v2), we continue the development of a comprehensive theory of Frobenius liftings modulo $p^2$. We study compatibility of divisors and closed subschemes with Frobenius liftings, Frobenius liftings of blow-ups, descent under quotients by some group actions, stability under base change, and the properties of associated F-splittings. Consequently, we characterise Frobenius liftable surfaces and Fano threefolds, confirming the conjecture stated in our previous paper.