{"paper":{"title":"The filled Julia set of a Drinfeld module and uniform bounds for torsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrick Ingram","submitted_at":"2012-10-10T20:54:28Z","abstract_excerpt":"If M is a Drinfeld module over a local function field L, we may view M as a dynamical system, and consider its filled Julia set J. If J^0 is the connected component of the identity, relative to the Berkovich topology, we give a characterisation of the component module J/J^0 which is analogous to the Kodaira-Neron characterisation of the special fibre of a Neron model of an elliptic curve over a non-archimedean field. In particular, if L is the fraction field of a discrete valuation ring, then the component module is finite, and moreover trivial in the case of good reduction.\n  In the context o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3059","kind":"arxiv","version":2},"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"}