{"paper":{"title":"de Rham theory and locally analytic vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gal Porat, Hui Gao, L\\'eo Poyeton","submitted_at":"2026-08-01T19:52:40Z","abstract_excerpt":"Let $K_\\infty/K$ be a $p$-adic Lie extension of a $p$-adic field $K$. We study the subring of pro-analytic vectors in the de Rham period ring $\\mathbf{B}_{\\mathrm{dR}}^+(K_\\infty)$. We show that the pro-analytic subring admits a Galois-equivariant isomorphism with a formal power series ring $\\widehat{K}_{\\infty}^{\\mathrm{la}} [[t_{K_\\infty}]]$ if and only if $K_\\infty$ satisfies a certain orientability condition, which says that the $\\widehat{K}_\\infty$-level Sen operator admits a Galois-equivariant $\\mathbf{B}_{\\mathrm{dR}}^+$-lift. A key input is the vanishing of higher locally analytic vect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00845","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.00845/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"}