{ "id": "2405.17118", "version": "v1", "published": "2024-05-27T12:35:13.000Z", "updated": "2024-05-27T12:35:13.000Z", "title": "On $ψ$-lattices in modular $(\\varphi,Γ)$-modules", "authors": [ "Elmar Große-Klönne" ], "comment": "14 pages", "journal": "Perfectoid spaces, Springer, Singapore (2022), ISBN:978-981-16-7120-3", "categories": [ "math.NT" ], "abstract": "Let $F/{\\mathbb Q}_p$ be a finite field extension, let $k$ be a finite field extension of the residue field of $F$. Generalizing the $\\psi$-lattices which Colmez constructed in \\'{e}tale $(\\varphi,\\Gamma)$-modules over $k[[t]][t^{-1}]$, we define, study and exemplify $\\psi$-lattices in \\'{e}tale $(\\varphi,\\Gamma)$-modules over $k[[t_1,\\ldots,t_d]][\\prod_it_i^{-1}]$ for arbitrary $d\\in{\\mathbb N}$.", "revisions": [ { "version": "v1", "updated": "2024-05-27T12:35:13.000Z" } ], "analyses": { "subjects": [ "11F80" ], "keywords": [ "finite field extension", "residue field" ], "tags": [ "journal article" ], "note": { "typesetting": "TeX", "pages": 14, "language": "en", "license": "arXiv", "status": "editable" } } }