--- DOAJ_listed: '1' OA_place: publisher OA_type: gold _id: '20043' abstract: - lang: eng text: We establish an isomorphism of complex K-theory of the moduli space M of “SL n​ ”-Higgs bundles of degree d and rank n (in the sense of Hausel–Thaddeus) and twisted complex K-theory of the orbifold M of PGL n​ -Higgs bundles of degree e, where (n,d)=(n,e)=1. Along the way, we prove the vanishing of torsion for H ∗ ( M ) and certain twisted complex K-theory groups of M . We also extend Arinkin’s autoduality of compactified Jacobian to a derived equivalence between SL n​ - and PGL n​ -Hitchin systems over the elliptic locus. In the appendix, we develop a formalism of G-sheaves of spectra, generalising equivariant homotopy theory to a relative setting. acknowledgement: "It is a pleasure to thank Tom Baird for sharing his insights about vanishing of torsion for H.M{1\r\n2/. Furthermore, we would like to thank him for bringing [25] to our attention. We also thank Alexander Kupers for enlightening conversations about the Atiyah–Hirzebruch spectral sequence and for pointing out a reference. We are grateful to Victoria Hoskins and Simon Pepin-Lehalleur for sharing a preprint of their recent paper on a motivic version of topological mirror symmetry and for useful remarks on Section 6. Anne Larsen pointed out that our previous proof Lemma 4.5 was incomplete, we thank her for bringing this to our attention. We are grateful to the anonymous referee for many valuable comments that have improved the paper tremendously. The report we received was one of the most detailed referee report either of us has ever seen. We thank them for their hard work and the resulting contribution to this paper. Michael Groechenig was supported by an NSERC discovery grant and an Alfred P. Sloan\r\nfellowship. Shiyu Shen has received funding from the European Union’s Horizon 2020 research\r\nand innovation program under the Marie Skłodowska-Curie grant agreement No. 101034413." article_processing_charge: Yes article_type: original arxiv: 1 author: - first_name: Michael full_name: Groechenig, Michael last_name: Groechenig - first_name: Shiyu full_name: Shen, Shiyu id: 544cccd3-9005-11ec-87bc-94aef1c5b814 last_name: Shen orcid: 0000-0002-4444-8718 citation: ama: Groechenig M, Shen S. Complex K-theory of moduli spaces of Higgs bundles. Journal of the European Mathematical Society. 2025. doi:10.4171/jems/1601 apa: Groechenig, M., & Shen, S. (2025). Complex K-theory of moduli spaces of Higgs bundles. Journal of the European Mathematical Society. EMS Press. https://doi.org/10.4171/jems/1601 chicago: Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of Higgs Bundles.” Journal of the European Mathematical Society. EMS Press, 2025. https://doi.org/10.4171/jems/1601. ieee: M. Groechenig and S. Shen, “Complex K-theory of moduli spaces of Higgs bundles,” Journal of the European Mathematical Society. EMS Press, 2025. ista: Groechenig M, Shen S. 2025. Complex K-theory of moduli spaces of Higgs bundles. Journal of the European Mathematical Society. mla: Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of Higgs Bundles.” Journal of the European Mathematical Society, EMS Press, 2025, doi:10.4171/jems/1601. short: M. Groechenig, S. Shen, Journal of the European Mathematical Society (2025). corr_author: '1' date_created: 2025-07-21T07:54:50Z date_published: 2025-03-20T00:00:00Z date_updated: 2026-06-16T14:34:30Z day: '20' ddc: - '510' department: - _id: TaHa doi: 10.4171/jems/1601 ec_funded: 1 external_id: arxiv: - '2212.10695' isi: - '001608254800001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.4171/JEMS/1601 month: '03' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Journal of the European Mathematical Society publication_identifier: eissn: - 1435-9863 issn: - 1435-9855 publication_status: epub_ahead publisher: EMS Press quality_controlled: '1' status: public title: Complex K-theory of moduli spaces of Higgs bundles type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '14986' abstract: - lang: eng text: We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k). Let k be an algebraically closed field of characteristic p>n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bunn,P the moduli stack of (quasi-)parabolic vector bundles on X, and by Locn,P the moduli stack of parabolic flat connections such that the residue is nilpotent with respect to the parabolic reduction at each marked point. We construct an equivalence between the bounded derived category Db(Qcoh(Loc0n,P)) of quasi-coherent sheaves on an open substack Loc0n,P⊂Locn,P, and the bounded derived category Db(D0Bunn,P-mod) of D0Bunn,P-modules, where D0Bunn,P is a localization of DBunn,P the sheaf of crystalline differential operators on Bunn,P. Thus we extend the work of Bezrukavnikov-Braverman to the tamely ramified case. We also prove a correspondence between flat connections on X with regular singularities and meromorphic Higgs bundles on the Frobenius twist X(1) of X with first order poles . acknowledgement: "This work was supported by the NSF [DMS-1502125to S.S.]; and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement [101034413 to S.S.].\r\nI would like to thank my advisor Tom Nevins for many helpful discussions on this subject and for his comments on this paper. I would like to thank Christopher Dodd, Michael Groechenig, and Tamas Hausel for helpful conversations. I would like to thank Tsao-Hsien Chen for useful comments on an earlier version of this paper." article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Shiyu full_name: Shen, Shiyu id: 544cccd3-9005-11ec-87bc-94aef1c5b814 last_name: Shen orcid: 0000-0002-4444-8718 citation: ama: Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024;2024(7):6176-6208. doi:10.1093/imrn/rnae005 apa: Shen, S. (2024). Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae005 chicago: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae005. ieee: S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,” International Mathematics Research Notices, vol. 2024, no. 7. Oxford University Press, pp. 6176–6208, 2024. ista: Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024(7), 6176–6208. mla: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices, vol. 2024, no. 7, Oxford University Press, 2024, pp. 6176–208, doi:10.1093/imrn/rnae005. short: S. Shen, International Mathematics Research Notices 2024 (2024) 6176–6208. corr_author: '1' date_created: 2024-02-14T12:16:17Z date_published: 2024-04-01T00:00:00Z date_updated: 2025-09-09T08:30:06Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1093/imrn/rnae005 ec_funded: 1 external_id: arxiv: - '1810.12491' isi: - '001157898100001' file: - access_level: open_access checksum: e3cd31ebb2e79b5b1f34d1c4ac9f5b0f content_type: application/pdf creator: dernst date_created: 2024-07-22T11:41:57Z date_updated: 2024-07-22T11:41:57Z file_id: '17308' file_name: 2024_IMRN_Shen.pdf file_size: 1488981 relation: main_file success: 1 file_date_updated: 2024-07-22T11:41:57Z has_accepted_license: '1' intvolume: ' 2024' isi: 1 issue: '7' keyword: - General Mathematics language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 6176-6208 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: '1' status: public title: Tamely ramified geometric Langlands correspondence in positive characteristic 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2024 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '15248' abstract: - lang: eng text: Applying the technique of p-adic integration, we prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic Higgs bundles for the structure groups SLn and PGLn, building on previous work of Groechenig-Wyss-Ziegler on the non-parabolic case. We also prove the E-polynomial of the smooth moduli space of parabolic GLn-Higgs bundles is independent of the degree of the underlying vector bundles. acknowledgement: Shiyu Shen has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 101034413. article_number: '109616' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Shiyu full_name: Shen, Shiyu id: 544cccd3-9005-11ec-87bc-94aef1c5b814 last_name: Shen orcid: 0000-0002-4444-8718 citation: ama: Shen S. Mirror symmetry for parabolic Higgs bundles via p-adic integration. Advances in Mathematics. 2024;443(5). doi:10.1016/j.aim.2024.109616 apa: Shen, S. (2024). Mirror symmetry for parabolic Higgs bundles via p-adic integration. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2024.109616 chicago: Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.” Advances in Mathematics. Elsevier, 2024. https://doi.org/10.1016/j.aim.2024.109616. ieee: S. Shen, “Mirror symmetry for parabolic Higgs bundles via p-adic integration,” Advances in Mathematics, vol. 443, no. 5. Elsevier, 2024. ista: Shen S. 2024. Mirror symmetry for parabolic Higgs bundles via p-adic integration. Advances in Mathematics. 443(5), 109616. mla: Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.” Advances in Mathematics, vol. 443, no. 5, 109616, Elsevier, 2024, doi:10.1016/j.aim.2024.109616. short: S. Shen, Advances in Mathematics 443 (2024). corr_author: '1' date_created: 2024-03-31T22:01:11Z date_published: 2024-05-01T00:00:00Z date_updated: 2025-09-04T13:21:18Z day: '01' ddc: - '510' department: - _id: TaHa doi: 10.1016/j.aim.2024.109616 ec_funded: 1 external_id: arxiv: - '2302.02817' isi: - '001216128200001' file: - access_level: open_access checksum: 68f2f08136ccf547891a16a2c0621e97 content_type: application/pdf creator: dernst date_created: 2024-07-22T12:10:03Z date_updated: 2024-07-22T12:10:03Z file_id: '17315' file_name: 2024_AdvancesMath_Shen.pdf file_size: 702889 relation: main_file success: 1 file_date_updated: 2024-07-22T12:10:03Z has_accepted_license: '1' intvolume: ' 443' isi: 1 issue: '5' language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Advances in Mathematics publication_identifier: eissn: - 1090-2082 issn: - 0001-8708 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Mirror symmetry for parabolic Higgs bundles via p-adic integration 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 443 year: '2024' ...