On the existence of F-crystals
R. Kottwitz, M. Rapoport
Abstract
Let (N,F) be an F-isocrystal, with associated Newton vector νin (Qn)+. To any lattice M in N (an F-crystal) is associated its Hodge vector μ(M) in (Zn)+. By Mazur's inequality we have μ(M)>= ν. We show that, conversely, for any μin (Zn)+ with μ>= ν, there exists a lattice M in N such that μ=μ(M). We also give variants of this existence theorem for symplectic F-isocrystals, and for periodic lattice chains.
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