{"paper":{"title":"On the existence of F-crystals","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"M. Rapoport, R. Kottwitz","submitted_at":"2002-02-22T13:56:00Z","abstract_excerpt":"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\n F-isocrystals, and for periodic lattice chains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202229","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}