Existence de filtrations admissibles sur des isocristaux

Original · EN

Let (D,phi) be an isocrystal over an algebraically closed field of characteristic p. Let Fᵇullet be a filtration on D. If Fᵇullet 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 Fᵇullet 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.