{"paper":{"title":"Crystalline lifts of semisimple $G$-valued Galois representations with fixed determinant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kensuke Aoki","submitted_at":"2024-12-31T04:04:46Z","abstract_excerpt":"For a finite extension $K/\\mathbb{Q}_p$ and a split reductive group $G$ over $\\mathcal{O}_K$, let $\\overline{\\rho} \\colon \\mathrm{Gal}_K \\to G(\\overline{\\mathbb{F}}_p)$ be a continuous quasi-semisimple mod $p$ $G$-valued representation of the absolute Galois group $\\mathrm{Gal}_K$. Let $\\overline{\\rho}^{\\mathrm{ab}}$ be the abelianization of $\\overline{\\rho}$ and fix a crystalline lift $\\psi$ of $\\overline{\\rho}^{\\mathrm{ab}}$. We show the existence of a crystalline lift $\\rho$ of $\\overline{\\rho}$ with regular Hodge-Tate weights such that the abelianization of $\\rho$ coincides with $\\psi$. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00259","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.00259/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"}