Computing isomorphism numbers of F-crystals by using level torsions
Abstract
The isomorphism number of an F-crystal (M, φ) over an algebraically closed field of positive characteristic is the smallest non-negative integer nM such that the nM-th level truncation of (M, φ) determines the isomorphism class of (M, φ). When (M, φ) is isoclinic, namely it has a unique Newton slopes λ, we provide an efficiently computable upper bound of nM in terms of the Hodge slopes of (M, φ) and λ. This is achieved by providing an upper bound of the level torsion of (M, φ) introduced by Vasiu. We also check that this upper bound is optimal for many families of isoclinic F-crystals that are of special interests (such as isoclinic F-crystals of K3 type).
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