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On the existence of F-crystals

R. Kottwitz·M. Rapoport
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Abstract

Let (N,F) be an F-isocrystal, with associated Newton vector \nu in (Q^n)_+. To any lattice M in N (an F-crystal) is associated its Hodge vector \mu(M) in (Z^n)_+. By Mazur's inequality we have \mu(M)>= \nu. We show that, conversely, for any \mu in (Z^n)_+ with \mu >= \nu, there exists a lattice M in N such that \mu=\mu(M). We also give variants of this existence theorem for symplectic F-isocrystals, and for periodic lattice chains.

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R. Kottwitz, M. Rapoport. 2002-02-22. On the existence of F-crystals. https://arxiv.org/abs/math/0202229

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