On isomorphism numbers of "$F$-crystals"

TL;DR

This paper proves that for $F$-crystals in equal characteristic, the isomorphism number equals the level torsion, confirming a conjecture by Vasiu in this setting.

Contribution

It establishes the equality of isomorphism number and level torsion for $F$-crystals in equal characteristic, confirming Vasiu's conjecture.

Findings

Isomorphism number equals level torsion for $F$-crystals in equal characteristic

Confirms Vasiu's conjecture in the equal characteristic case

Provides a key structural insight into $F$-crystals

Abstract

In this note, we show that for an ``$F$-crystal" (the equal characteristic analogue of $F$-crystals), its {\it isomorphism number} and its {\it level torsion} coincide. This confirms a conjure of Vasiu \cite{Va} in the equal characteristic case.