{"paper":{"title":"Modularity of fibres in rigid local systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Henri Darmon","submitted_at":"1999-05-01T00:00:00Z","abstract_excerpt":"It is believed that any p-adic Galois representation which is potentially semistable arises from a modular form. The main theorem of Wiles establishes this modularity when the representation in question satisfies various technical restrictions, together with the key hypothesis that its reduction modulo p arises itself from a modular form. This article explains how a strong version of Wiles' \"lifting theorem\" implies the modularity of all hypergeometric abelian varieties - so-called because their periods are expressed in terms of values of classical hypergeometric functions. While this strong v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9905208","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"}