{"paper":{"title":"The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC","math.RA"],"primary_cat":"math.QA","authors_text":"Myriam Mahaman","submitted_at":"2026-05-18T15:45:11Z","abstract_excerpt":"In a previous article, we showed that local projectivity is a sufficient condition for the existence of a bialgebroid structure on the ring of differential operators on an affine variety. In this note, we show using elementary methods that the ring of differential operators on a nodal curve is neither locally projective nor does it admit a bialgebroid structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18568","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/2605.18568/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.342925Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c99c3bf614020cc8362fcc3444e167f86198f6ce51989a73f96b9ab52ac322fd"},"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"}