{"paper":{"title":"Nilpotent cohomological Hall algebras of surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.QA","math.RT"],"primary_cat":"math.AG","authors_text":"Duiliu-Emanuel Diaconescu, Eric Vasserot, Francesco Sala, Mauro Porta, Olivier Schiffmann","submitted_at":"2025-02-25T09:39:43Z","abstract_excerpt":"This paper develops a framework for systematically studying cohomological \"Hecke operators\" associated with modifications of coherent sheaves on a smooth surface $X$ along a fixed proper curve $Z \\subset X$ (possibly singular and reducible), using the theory of cohomological Hall algebras.\n  More precisely, we construct a moduli stack of coherent sheaves $\\mathbf{Coh}(\\widehat{X}_Z)$ on $X$ with set-theoretic support $Z$ and we prove that its reduced is an Artin stack locally of finite type. This provides a vast generalization of the global nilpotent cone. Subsequently, we develop the needed b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19445","kind":"arxiv","version":3},"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/2502.19445/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"}