# Subtle Invariants of F-crystals

Available at Journal of Ramanujan Mathematical Society, 2014

Abstract: Vasiu proved that the level torsion lM of an F-crystal 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 nM of M and expected that in fact one always has nM = lM. In this paper, we prove that this equality holds.