Subtle Invariants of $F$-crystals

Abstract

Vasiu proved that the level torsion ${\ell }_{\mathcal{M}}$ of an $F$-crystal $\mathcal{M}$ over an algebraically closed field of characteristic $p>0$ is a non-negative integer that is an effectively computable upper bound of the isomorphism number $n_{\mathcal{M}}$ of $\mathcal{M}$ and expected that in fact one always has $n_{\mathcal{M}}={\ell }_{\mathcal{M}}$. In this paper, we prove that this equality holds.

Final accepted version at J. Ramanujan Math. Soc

References in corpus (4)

• Crystalline boundedness principle
• Reconstructing $p$-divisible groups from their truncations of small level
• Dimensions of group schemes of automorphisms of truncated Barsotti--Tate groups
• On isomorphism numbers of "$F$-crystals"

Cited by in corpus (2)

• On isomorphism numbers of "$F$-crystals"
• Minimal $F$-crystals and isomorphism numbers of isosimple $F$-crystals