Generic vanishing and classification of irregular surfaces in positive characteristics

TL;DR

This paper proves a generic vanishing theorem for certain algebraic surfaces in positive characteristic and applies it to classify surfaces of general type with specific invariants.

Contribution

It introduces a generic vanishing theorem in positive characteristic and uses it to classify irregular surfaces of general type with Euler characteristic 1.

Findings

Established a generic vanishing theorem for surfaces in characteristic p

Classified surfaces of general type with Euler characteristic 1 and high Albanese dimension

Extended vanishing techniques to positive characteristic settings

Abstract

We establish a generic vanishing theorem for surfaces in characteristic $p$ that lift to $W_2(k)$ and use it for surface classification of surfaces of general type with Euler characteristic 1 and large Albanese dimension.