{"paper":{"title":"Koszul duality for Iwasawa algebras modulo p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Claus Sorensen","submitted_at":"2019-02-25T21:52:12Z","abstract_excerpt":"In this article we establish a version of Koszul duality for filtered rings arising from $p$-adic Lie groups. Our precise setup is the following. We let $G$ be a uniform pro-$p$ group and consider its completed group algebra $\\Omega=k[\\![G]\\!]$ with coefficients in a finite field $k$ of characteristic $p$. It is known that $\\Omega$ carries a natural filtration and $\\text{gr} \\Omega=S(\\frak{g})$ where $\\frak{g}$ is the (abelian) Lie algebra of $G$ over $k$. One of our main results in this paper is that the Koszul dual $\\text{gr} \\Omega^!=\\bigwedge \\frak{g}^{\\vee}$ can be promoted to an $A_{\\inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09632","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"}