{"paper":{"title":"Multivariable period rings of $p$-adic false Tate curve extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yijun Yuan","submitted_at":"2025-05-29T23:16:46Z","abstract_excerpt":"Let $p\\geq 3$ be a prime number and $K$ be a finite extension of $\\mathbf{Q}_p$ with uniformizer $\\pi_K$. In this article, we introduce two multivariable period rings $\\mathbf{A}_{\\mathfrak{F},K}^{\\operatorname{np}}$ and $\\mathbf{A}_{\\mathfrak{F},K}^{\\operatorname{np},\\operatorname{c}}$ for the \\'etale $(\\varphi,\\Gamma_{\\mathfrak{F},K})$-modules of $p$-adic false Tate curve extension $K\\left(\\pi_K^{1/p^\\infty},\\zeta_{p^\\infty}\\right)$. Various properties of these rings are studied and as applications, we show that $(\\varphi,\\Gamma_{\\mathfrak{F},K})$-modules over these rings bridge $(\\varphi,\\G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24064","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/2505.24064/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"}