{"paper":{"title":"Beauville-Laszlo gluing of algebraic spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex Youcis, Piotr Achinger","submitted_at":"2024-10-27T16:28:07Z","abstract_excerpt":"For a complete discrete valuation field $K$, we show that one may always glue a separated formal algebraic space $\\mathfrak{X}$ over $\\mathcal{O}_K$ to a separated algebraic space $U$ over $K$ along an open immersion of rigid spaces $j\\colon \\mathfrak{X}^{\\rm rig}\\to U^{\\rm an}$, producing a separated algebraic space $X$ over $\\mathcal{O}_K$. This process gives rise to an equivalence between such `gluing triples' $(U,\\mathfrak{X},j)$ and separated algebraic spaces $X$ over $\\mathcal{O}_K$, which one might interpret as a version of the Beauville--Laszlo theorem for algebraic spaces rather than "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20500","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/2410.20500/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"}