{"paper":{"title":"Unit L-functions for \\'etale sheaves of modules over noncommutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Malte Witte","submitted_at":"2013-09-10T13:09:43Z","abstract_excerpt":"Let $s\\colon X\\rightarrow \\operatorname{Spec} \\mathbb{F}$ be a separated scheme of finite type over a finite field $\\mathbb{F}$ of characteristic $p$, let $\\Lambda$ be a not necessarily commutative $\\mathbb{Z}_p$-algebra with finitely many elements, and let $\\mathcal{F}^\\bullet$ be a perfect complex of $\\Lambda$-sheaves on the \\'etale site of $X$. We show that the ratio $L(\\mathcal{F}^\\bullet,T)/L(R s_!\\mathcal{F}^\\bullet,T)$, which is a priori an element of $K_1(\\Lambda[[T]])$, has a canonical preimage in $K_1(\\Lambda[T])$. We use this to prove a version of the noncommmutative Iwasawa main co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2493","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"}