{"paper":{"title":"Ideals of Rings of Differential Operators on Algebraic Curves (With an Appendix by George Wilson)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Oleg Chalykh, Yuri Berest","submitted_at":"2008-09-18T21:46:12Z","abstract_excerpt":"Let X be a complex smooth affine irreducible curve, and let D = D(X) be the ring of global differential operators on X. In this paper, we give a geometric classification of left ideals in $ D $ and study the natural action of the Picard group of D on the space J(D) of isomorphism classes of such ideals. We recall that, up to isomorphism in the Grothendieck group K_0(D), the ideals of D are classified by the Picard group of X: there is a natural fibration \\gamma: J(D) \\to Pic(X), whose fibres are the stable isomorphism classes of ideals of D (see \\cite{BW}). In this paper, we refine this classi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3258","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}