---
_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
citation:
  ama: Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic.
    <i>International Mathematics Research Notices</i>. 2024. doi:<a href="https://doi.org/10.1093/imrn/rnae005">10.1093/imrn/rnae005</a>
  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>
  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>.
  ieee: S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,”
    <i>International Mathematics Research Notices</i>. Oxford University Press, 2024.
  ista: Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive
    characteristic. International Mathematics Research Notices.
  mla: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive
    Characteristic.” <i>International Mathematics Research Notices</i>, Oxford University
    Press, 2024, doi:<a href="https://doi.org/10.1093/imrn/rnae005">10.1093/imrn/rnae005</a>.
  short: S. Shen, International Mathematics Research Notices (2024).
date_created: 2024-02-14T12:16:17Z
date_published: 2024-02-05T00:00:00Z
date_updated: 2024-02-19T10:22:44Z
day: '05'
department:
- _id: TaHa
doi: 10.1093/imrn/rnae005
ec_funded: 1
external_id:
  arxiv:
  - '1810.12491'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1093/imrn/rnae005
month: '02'
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: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: epub_ahead
publisher: Oxford University Press
quality_controlled: '1'
status: public
title: Tamely ramified geometric Langlands correspondence in positive characteristic
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...