{"paper":{"title":"Torsion representations arising from $(\\varphi,\\hat{G})$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yoshiyasu Ozeki","submitted_at":"2012-02-09T00:00:28Z","abstract_excerpt":"The notion of a $(\\varphi,\\hat{G})$-module is defined by Tong Liu in 2010 to classify lattices in semi-stable representations. In this paper, we study torsion $(\\varphi,\\hat{G})$-modules, and torsion p-adic representations associated with them, including the case where p=2. First we prove that the category of torsion p-adic representations arising from torsion $(\\varphi,\\hat{G})$-modules is an abelian category. Secondly, we construct a maximal (minimal) theory for $(\\varphi,\\hat{G})$-modules by using the theory of \\'etale $(\\varphi, \\hat{G})$-modules, essentially proved by Xavier Caruso, which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1858","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"}