{"paper":{"title":"A note on crystalline liftings in the $\\mathbb{Q}_p$ case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hui Gao","submitted_at":"2015-05-01T08:53:18Z","abstract_excerpt":"Let $p>2$ be a prime. Let $\\rho$ be a crystalline representation of $G_{\\mathbb{Q}_p}$ with distinct Hodge-Tate weights in $[0, p]$, such that its reduction $\\overline \\rho$ is upper triangular. Under certain conditions, we prove that $\\overline \\rho$ has an upper triangular crystalline lift $\\rho'$ such that $\\mathrm{HT}(\\rho')=\\mathrm{HT}(\\rho)$. The method is based on the author's previous work, combined with an inspiration from the work of Breuil-Herzig."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00125","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":""},"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"}