{"paper":{"title":"Level lowering: a Mazur principle in higher dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pascal Boyer","submitted_at":"2019-08-19T21:11:41Z","abstract_excerpt":"For a maximal ideal $\\mathfrak m$ of some anemic Hecke algebra $\\mathbb{T}^S_\\xi$ of a similitude group of signature $(1,d-1)$, one can associate a Galois $\\overline{\\mathbb F}_l$-representation $\\overline \\rho_{\\mathfrak m}$ as well as a Galois $\\mathbb{T}_{\\xi,\\mathfrak m}^S$-representation $\\rho_{\\mathfrak m}$.For $l\\geq d$, on can also define a monodromy operator $\\overline N_{\\mathfrak m}$ as well as $N_{\\widetilde{\\mathfrak m}}$ for every prime ideal $\\widetilde{\\mathfrak m} \\subset \\mathfrak m$, giving rise to partitions $\\underline{\\bar d_{\\mathfrak m}}$ and $\\underline d_{\\widetilde{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07073","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07073/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}