{"paper":{"title":"Duality for relative logarithmic de Rham-Witt sheaves on semistable schemes over $\\mathbb{F}_q[[t]]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yigeng Zhao","submitted_at":"2016-11-26T17:06:13Z","abstract_excerpt":"We study duality theorems for the relative logarithmic de Rham-Witt sheaves on semi-stable schemes $X$ over a local ring $\\mathbb{F}_q[[t]]$, where $\\mathbb{F}_q$ is a finite field. As an application, we obtain a new filtration on the maximal abelian quotient $\\pi^{\\text{ab}}_1(U)$ of the \\'etale fundamental groups $\\pi_1(U)$ of an open subscheme $U \\subseteq X$, which gives a measure of ramification along a divisor $D$ with normal crossing and $\\text{Supp}(D) \\subseteq X-U$. This filtration coincides with the Brylinski-Kato-Matsuda filtration in the relative dimension zero case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08722","kind":"arxiv","version":2},"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"}