{"corr_author":"1","main_file_link":[{"url":"https://doi.org/10.4171/JEMS/1601","open_access":"1"}],"oa":1,"publication":"Journal of the European Mathematical Society","oa_version":"Published Version","publication_status":"epub_ahead","DOAJ_listed":"1","_id":"20043","date_updated":"2025-07-22T09:56:50Z","department":[{"_id":"TaHa"}],"doi":"10.4171/jems/1601","article_type":"original","OA_place":"publisher","day":"20","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","author":[{"full_name":"Groechenig, Michael","last_name":"Groechenig","first_name":"Michael"},{"id":"544cccd3-9005-11ec-87bc-94aef1c5b814","orcid":"0000-0002-4444-8718","first_name":"Shiyu","last_name":"Shen","full_name":"Shen, Shiyu"}],"external_id":{"arxiv":["2212.10695"]},"month":"03","date_published":"2025-03-20T00:00:00Z","ec_funded":1,"title":"Complex K-theory of moduli spaces of Higgs bundles","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_type":"gold","publisher":"European Mathematical Society","citation":{"ieee":"M. Groechenig and S. Shen, “Complex K-theory of moduli spaces of Higgs bundles,” <i>Journal of the European Mathematical Society</i>. European Mathematical Society, 2025.","ista":"Groechenig M, Shen S. 2025. Complex K-theory of moduli spaces of Higgs bundles. Journal of the European Mathematical Society.","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>","short":"M. Groechenig, S. Shen, Journal of the European Mathematical Society (2025).","mla":"Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of Higgs Bundles.” <i>Journal of the European Mathematical Society</i>, European Mathematical Society, 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>. European Mathematical Society, 2025. <a href=\"https://doi.org/10.4171/jems/1601\">https://doi.org/10.4171/jems/1601</a>.","apa":"Groechenig, M., &#38; Shen, S. (2025). Complex K-theory of moduli spaces of Higgs bundles. <i>Journal of the European Mathematical Society</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/jems/1601\">https://doi.org/10.4171/jems/1601</a>"},"date_created":"2025-07-21T07:54:50Z","type":"journal_article","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"}],"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."}],"year":"2025","status":"public","arxiv":1}