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Existence de filtrations admissibles sur des isocristaux

J. -M. Fontaine·M. Rapoport
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Abstract

Let (D,phi) be an isocrystal over an algebraically closed field of characteristic p. Let F^bullet be a filtration on D. If F^bullet is (weakly) admissible, its type vector is greater or equal to the slope vector of (D,phi). We prove that conversely, give a type mu greater or equal to the slope vector of (D,phi), there exists an admissible filtration F^bullet on D of type vector equal to mu. We also give a group theoretic version of this statement and relate it to the existence of lattices M in D with mu(M)=mu.

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J. -M. Fontaine, M. Rapoport. 2002-04-24. Existence de filtrations admissibles sur des isocristaux. https://arxiv.org/abs/math/0204293

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