[{"title":"Complex K-theory of moduli spaces of Higgs bundles","author":[{"last_name":"Groechenig","first_name":"Michael","full_name":"Groechenig, Michael"},{"orcid":"0000-0002-4444-8718","first_name":"Shiyu","id":"544cccd3-9005-11ec-87bc-94aef1c5b814","last_name":"Shen","full_name":"Shen, Shiyu"}],"isi":1,"arxiv":1,"ec_funded":1,"type":"journal_article","date_published":"2025-03-20T00:00:00Z","DOAJ_listed":"1","ddc":["510"],"publication":"Journal of the European Mathematical Society","publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"quality_controlled":"1","article_processing_charge":"Yes","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.","OA_place":"publisher","year":"2025","month":"03","_id":"20043","citation":{"ista":"Groechenig M, Shen S. 2025. Complex K-theory of moduli spaces of Higgs bundles. Journal of the European Mathematical Society.","apa":"Groechenig, M., &#38; Shen, S. (2025). Complex K-theory of moduli spaces of Higgs bundles. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1601\">https://doi.org/10.4171/jems/1601</a>","short":"M. Groechenig, S. Shen, Journal of the European Mathematical Society (2025).","ieee":"M. Groechenig and S. Shen, “Complex K-theory of moduli spaces of Higgs bundles,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025.","mla":"Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of Higgs Bundles.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1601\">10.4171/jems/1601</a>.","ama":"Groechenig M, Shen S. Complex K-theory of moduli spaces of Higgs bundles. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1601\">10.4171/jems/1601</a>","chicago":"Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of Higgs Bundles.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jems/1601\">https://doi.org/10.4171/jems/1601</a>."},"date_updated":"2026-06-16T14:34:30Z","publisher":"EMS Press","corr_author":"1","language":[{"iso":"eng"}],"oa_version":"Published Version","OA_type":"gold","abstract":[{"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.","lang":"eng"}],"date_created":"2025-07-21T07:54:50Z","article_type":"original","external_id":{"arxiv":["2212.10695"],"isi":["001608254800001"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1601"}],"oa":1,"status":"public","publication_status":"epub_ahead","day":"20","project":[{"call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"}],"doi":"10.4171/jems/1601","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"TaHa"}]},{"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.","OA_place":"publisher","year":"2024","month":"04","_id":"14986","date_updated":"2025-09-09T08:30:06Z","page":"6176-6208","citation":{"chicago":"Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnae005\">https://doi.org/10.1093/imrn/rnae005</a>.","ista":"Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024(7), 6176–6208.","short":"S. Shen, International Mathematics Research Notices 2024 (2024) 6176–6208.","apa":"Shen, S. (2024). Tamely ramified geometric Langlands correspondence in positive characteristic. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnae005\">https://doi.org/10.1093/imrn/rnae005</a>","ieee":"S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,” <i>International Mathematics Research Notices</i>, vol. 2024, no. 7. Oxford University Press, pp. 6176–6208, 2024.","ama":"Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic. <i>International Mathematics Research Notices</i>. 2024;2024(7):6176-6208. doi:<a href=\"https://doi.org/10.1093/imrn/rnae005\">10.1093/imrn/rnae005</a>","mla":"Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” <i>International Mathematics Research Notices</i>, vol. 2024, no. 7, Oxford University Press, 2024, pp. 6176–208, doi:<a href=\"https://doi.org/10.1093/imrn/rnae005\">10.1093/imrn/rnae005</a>."},"publisher":"Oxford University Press","corr_author":"1","language":[{"iso":"eng"}],"file":[{"file_id":"17308","creator":"dernst","file_name":"2024_IMRN_Shen.pdf","file_size":1488981,"checksum":"e3cd31ebb2e79b5b1f34d1c4ac9f5b0f","date_created":"2024-07-22T11:41:57Z","date_updated":"2024-07-22T11:41:57Z","access_level":"open_access","success":1,"content_type":"application/pdf","relation":"main_file"}],"title":"Tamely ramified geometric Langlands correspondence in positive characteristic","author":[{"orcid":"0000-0002-4444-8718","full_name":"Shen, Shiyu","id":"544cccd3-9005-11ec-87bc-94aef1c5b814","first_name":"Shiyu","last_name":"Shen"}],"isi":1,"arxiv":1,"ec_funded":1,"type":"journal_article","has_accepted_license":"1","date_published":"2024-04-01T00:00:00Z","ddc":["510"],"publication":"International Mathematics Research Notices","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","issue":"7","PlanS_conform":"1","oa":1,"file_date_updated":"2024-07-22T11:41:57Z","keyword":["General Mathematics"],"status":"public","publication_status":"published","project":[{"call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"}],"day":"01","doi":"10.1093/imrn/rnae005","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"TaHa"}],"oa_version":"Published Version","OA_type":"hybrid","abstract":[{"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 .","lang":"eng"}],"date_created":"2024-02-14T12:16:17Z","volume":2024,"article_type":"original","external_id":{"arxiv":["1810.12491"],"isi":["001157898100001"]},"tmp":{"short":"CC BY (4.0)","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)"},"scopus_import":"1","intvolume":"      2024"},{"article_processing_charge":"Yes (via OA deal)","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"quality_controlled":"1","publication":"Advances in Mathematics","ddc":["510"],"date_published":"2024-05-01T00:00:00Z","has_accepted_license":"1","type":"journal_article","isi":1,"arxiv":1,"ec_funded":1,"title":"Mirror symmetry for parabolic Higgs bundles via p-adic integration","author":[{"last_name":"Shen","first_name":"Shiyu","id":"544cccd3-9005-11ec-87bc-94aef1c5b814","full_name":"Shen, Shiyu","orcid":"0000-0002-4444-8718"}],"file":[{"creator":"dernst","file_id":"17315","checksum":"68f2f08136ccf547891a16a2c0621e97","file_size":702889,"date_created":"2024-07-22T12:10:03Z","file_name":"2024_AdvancesMath_Shen.pdf","success":1,"date_updated":"2024-07-22T12:10:03Z","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publisher":"Elsevier","corr_author":"1","language":[{"iso":"eng"}],"month":"05","_id":"15248","date_updated":"2025-09-04T13:21:18Z","citation":{"chicago":"Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.” <i>Advances in Mathematics</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.aim.2024.109616\">https://doi.org/10.1016/j.aim.2024.109616</a>.","ieee":"S. Shen, “Mirror symmetry for parabolic Higgs bundles via p-adic integration,” <i>Advances in Mathematics</i>, vol. 443, no. 5. Elsevier, 2024.","ama":"Shen S. Mirror symmetry for parabolic Higgs bundles via p-adic integration. <i>Advances in Mathematics</i>. 2024;443(5). doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109616\">10.1016/j.aim.2024.109616</a>","mla":"Shen, Shiyu. “Mirror Symmetry for Parabolic Higgs Bundles via P-Adic Integration.” <i>Advances in Mathematics</i>, vol. 443, no. 5, 109616, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109616\">10.1016/j.aim.2024.109616</a>.","ista":"Shen S. 2024. Mirror symmetry for parabolic Higgs bundles via p-adic integration. Advances in Mathematics. 443(5), 109616.","apa":"Shen, S. (2024). Mirror symmetry for parabolic Higgs bundles via p-adic integration. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2024.109616\">https://doi.org/10.1016/j.aim.2024.109616</a>","short":"S. Shen, Advances in Mathematics 443 (2024)."},"year":"2024","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.","OA_place":"publisher","intvolume":"       443","scopus_import":"1","external_id":{"arxiv":["2302.02817"],"isi":["001216128200001"]},"tmp":{"short":"CC BY (4.0)","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)"},"volume":443,"date_created":"2024-03-31T22:01:11Z","article_type":"original","article_number":"109616","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."}],"OA_type":"hybrid","oa_version":"Published Version","doi":"10.1016/j.aim.2024.109616","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"TaHa"}],"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"day":"01","publication_status":"published","status":"public","file_date_updated":"2024-07-22T12:10:03Z","oa":1,"issue":"5"}]