{"paper":{"title":"Lattices in potentially semi-stable representations and weak $(\\varphi,\\hat{G})$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yoshiyasu Ozeki","submitted_at":"2015-02-02T02:02:35Z","abstract_excerpt":"Let $p$ be a prime number and $r$ a non-negative integer. In this paper, we prove that there exists an anti-equivalence between the category of weak $(\\varphi,\\hat{G})$-modules of height $r$ and a certain subcategory of the category of Galois stable lattices in potentially semi-stable $p$-adic representations with Hodge-Tate weights in $[0,r]$. This gives an answer to a Tong Liu's question about the essential image of a functor on weak $(\\varphi,\\hat{G})$-modules. For a proof, following Liu's methods, we construct linear algebraic data which classify lattices in potentially semi-stable represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00340","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":""},"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"}