{"paper":{"title":"The Brian\\c{c}on-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Karl Schwede, Linquan Ma, Peter M. McDonald, Rebecca R.G.","submitted_at":"2025-10-13T15:39:31Z","abstract_excerpt":"Suppose $J = (f_1, \\dots, f_n)$ is an $n$-generated ideal in any ring $R$. We prove a general Brian\\c{c}on-Skoda-type containment relating the integral closure $\\overline{J^{n+k-1}}$ with ordinary powers $J^k$. We prove that our result implies the full Brian\\c{c}on-Skoda containment $\\overline{J^{n+k-1}} \\subseteq J^k$ for pseudo-rational singularities (for instance regular rings), and even for the weaker condition of birational derived splinters. Our methods also yield the containment $\\overline{J^{n+k}} \\subseteq J^k$ for Du Bois singularities and even for a characteristic-free generalizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.11540","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/2510.11540/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"}