---
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. <i>Journal
    of the European Mathematical Society</i>. 2025. doi:<a href="https://doi.org/10.4171/jems/1601">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>. EMS Press.
    <a href="https://doi.org/10.4171/jems/1601">https://doi.org/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>.
  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.
  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.” <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>.
  short: M. Groechenig, S. Shen, Journal of the European Mathematical Society (2025).
corr_author: '1'
das_tickbox: '1'
date_created: 2025-07-21T07:54:50Z
date_published: 2025-03-20T00:00:00Z
date_updated: 2026-07-23T11:16:00Z
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
mathsc:
- 14H60
- 19L50
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'
...