{"paper":{"title":"Ramification and cleanliness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ahmed Abbes, Takeshi Saito","submitted_at":"2010-07-22T12:56:24Z","abstract_excerpt":"This article is devoted to studying the ramification of Galois torsors and of $\\ell$-adic sheaves in characteristic $p>0$ (with $\\ell\\not=p$). Let $k$ be a perfect field of characteristic $p>0$, $X$ be a smooth, separated and quasi-compact $k$-scheme, $D$ be a simple normal crossing divisor on $X$, $U=X-D$, $\\Lambda$ be a finite local ${\\mathbb Z}_\\ell$-algebra, $F$ be a locally constant constructible sheaf of $\\Lambda$-modules on $U$. We introduce a boundedness condition on the ramification of $F$ along $D$, and study its main properties, in particular, some specialization properties that lea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3873","kind":"arxiv","version":3},"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"}