# Journal of the Ramanujan Mathematical Society

Volume 29, Issue 4, December 2014  pp. 413–458.

Subtle invariants of F-crystals

Authors:  Xiao Xiao
Author institution:Mathematics Department, Utica College, 1600 Burrstone Road, Utica, NY 13502

Summary:  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 n M of M and expected that in fact one always has nM = l M. In~this paper, we prove that this equality holds.