--- _id: '7683' abstract: - lang: eng text: For any free oriented Borel–Moore homology theory A, we construct an associative product on the A-theory of the stack of Higgs torsion sheaves over a projective curve C. We show that the resulting algebra AHa0C admits a natural shuffle presentation, and prove it is faithful when A is replaced with usual Borel–Moore homology groups. We also introduce moduli spaces of stable triples, heavily inspired by Nakajima quiver varieties, whose A-theory admits an AHa0C-action. These triples can be interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action of AHa0C on the cohomology of Hilbert schemes of points on T∗C. article_number: '30' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sasha full_name: Minets, Sasha id: 3E7C5304-F248-11E8-B48F-1D18A9856A87 last_name: Minets orcid: 0000-0003-3883-1806 citation: ama: Minets S. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 2020;26(2). doi:10.1007/s00029-020-00553-x apa: Minets, S. (2020). Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. Springer Nature. https://doi.org/10.1007/s00029-020-00553-x chicago: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series. Springer Nature, 2020. https://doi.org/10.1007/s00029-020-00553-x. ieee: S. Minets, “Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces,” Selecta Mathematica, New Series, vol. 26, no. 2. Springer Nature, 2020. ista: Minets S. 2020. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 26(2), 30. mla: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series, vol. 26, no. 2, 30, Springer Nature, 2020, doi:10.1007/s00029-020-00553-x. short: S. Minets, Selecta Mathematica, New Series 26 (2020). date_created: 2020-04-26T22:00:44Z date_published: 2020-04-15T00:00:00Z date_updated: 2023-08-21T06:14:58Z day: '15' ddc: - '510' department: - _id: TaHa doi: 10.1007/s00029-020-00553-x external_id: arxiv: - '1801.01429' isi: - '000526036400001' file: - access_level: open_access checksum: 2368c4662629b4759295eb365323b2ad content_type: application/pdf creator: dernst date_created: 2020-04-28T10:57:58Z date_updated: 2020-07-14T12:48:02Z file_id: '7690' file_name: 2020_SelectaMathematica_Minets.pdf file_size: 792469 relation: main_file file_date_updated: 2020-07-14T12:48:02Z has_accepted_license: '1' intvolume: ' 26' isi: 1 issue: '2' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '04' oa: 1 oa_version: Published Version project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Selecta Mathematica, New Series publication_identifier: eissn: - '14209020' issn: - '10221824' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 26 year: '2020' ...