{"paper":{"title":"Infinitely ramified Galois representations","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ravi Ramakrishna","submitted_at":"2000-03-01T00:00:00Z","abstract_excerpt":"In this paper we show how to construct, for most p >= 5, two types of surjective representations\n  \\rho:G_Q=Gal(\\bar{Q}/Q) -> GL_2(Z_p)\n  that are ramified at an infinite number of primes. The image of inertia at almost all of these primes will be torsion-free. The first construction is unconditional. The catch is that we cannot say whether\n  \\rho|_{G_p=Gal(\\bar{Q_p}/Q_p)\n  is crystalline or even potentially semistable. The second construction assumes the Generalized Riemann Hypothesis (GRH). With this assumption we can further arrange that \\rho|_{G_p} is crystalline at p. We remark that infin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0003241","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"}