2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63901Let (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.10 pages, AMS-TeXNumber TheoryAlgebraic GeometryPrimary 11S25; Secondary 14L05; 14F30text