{"paper":{"title":"Loose crystalline lifts and overconvergence of \\'etale $(\\varphi, \\tau)$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hui Gao, Tong Liu","submitted_at":"2016-06-23T07:34:53Z","abstract_excerpt":"Let $p$ be a prime, $K$ a finite extension of $\\mathbb Q_p$, and let $G_K$ be the absolute Galois group of $K$. The category of \\'etale $(\\varphi, \\tau)$-modules is equivalent to the category of $p$-adic Galois representations of $G_K$. In this paper, we show that all \\'etale $(\\varphi, \\tau)$-modules are overconvergent; this answers a question of Caruso. Our result is an analogy of the classical overconvergence result of Cherbonnier and Colmez in the setting of \\'etale $(\\varphi, \\Gamma)$-modules. However, our method is completely different from theirs. Indeed, we first show that all $p$-powe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07216","kind":"arxiv","version":3},"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"}