{"paper":{"title":"Weibel vanishing and the projective bundle formula for mixed characteristic motivic cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.NT"],"primary_cat":"math.AG","authors_text":"Tess Bouis","submitted_at":"2025-07-22T11:58:01Z","abstract_excerpt":"We prove that the motivic cohomology of mixed characteristic schemes, introduced in our previous work, satisfies various expected properties of motivic cohomology, including a motivic refinement of Weibel's vanishing in algebraic $K$-theory, the projective bundle formula, a comparison to Milnor $K$-theory, and a universal characterisation in terms of pro cdh descent. These results extend those of Elmanto--Morrow to schemes which are not necessarily defined over a field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16501","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.16501/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"}