{"paper":{"title":"The arc-topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Akhil Mathew, Bhargav Bhatt","submitted_at":"2018-07-12T17:01:06Z","abstract_excerpt":"We study a Grothendieck topology on schemes which we call the $\\mathrm{arc}$-topology. This topology is a refinement of the $v$-topology (the pro-version of Voevodsky's $h$-topology) where covers are tested via rank $\\leq 1$ valuation rings. Functors which are $\\mathrm{arc}$-sheaves are forced to satisfy a variety of glueing conditions such as excision in the sense of algebraic $K$-theory.\n  We show that \\'etale cohomology is an $\\mathrm{arc}$-sheaf and deduce various pullback squares in \\'etale cohomology. Using $\\mathrm{arc}$-descent, we reprove the Gabber-Huber affine analog of proper base "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04725","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1807.04725/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}