{"paper":{"title":"Birational and $\\mathbf{A}^1$-invariant lattices in the cohomology of the structure sheaf over non-archimedean fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alberto Merici, Kay R\\\"ulling, Shuji Saito","submitted_at":"2026-05-21T06:34:46Z","abstract_excerpt":"We show that the cohomology of the structure sheaf of smooth and proper schemes over a complete non-archimedean field $K$ of characteristic zero, can be refined to an $\\mathbf{A}^1$-invariant cohomology theory of smooth (not necessarily proper) schemes over $K$ with values in $\\mathcal{O}_K$-lattices, and the same holds for $K$ of positive characteristic in dimensions at most $3$. As one application, we obtain that the automorphism group of the function field of a proper smooth variety $X$ of dimension at most 3 over a field of positive characteristic acts quasi-unipotently on the cohomology o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22046","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/2605.22046/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"}