An explicit formula for the Artin invariant of smooth K3 hypersurfaces

TL;DR

This paper derives an explicit formula for the Artin invariant of smooth K3 hypersurfaces using quasi-$F$-splitting, providing a clear characterization and computational method.

Contribution

It introduces a new explicit formula for the Artin invariant of smooth K3 hypersurfaces based on quasi-$F$-splitting properties.

Findings

Explicit formula for the Artin invariant derived

Characterization of the invariant via quasi-$F$-splitting

Application to computing the invariant explicitly

Abstract

We characterize the Artin invariant of a smooth K3 hypersurface in terms of quasi-$F$-splitting. As an application, we obtain an explicit formula for this invariant.