{"paper":{"title":"Variation of Heegner points in Hida families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Howard","submitted_at":"2012-02-28T20:53:27Z","abstract_excerpt":"Given a weight two modular form f with associated p-adic Galois representation V_f, for certain quadratic imaginary fields K one can construct canonical classes in the Galois cohomology of V_f by taking the Kummer images of Heegner points on the modular abelian variety attached to f. We show that these classes can be interpolated as f varies in a Hida family, and construct an Euler system of big Heegner points for Hida's universal ordinary deformation of V_f. We show that the specialization of this big Euler system to any form in the Hida family is nontrivial, extending results of Cornut and V"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6358","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"}