Tamely ramified geometric Langlands correspondence in positive characteristic

Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices.

Download (ext.)

Journal Article | Epub ahead of print | English
Department
Abstract
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 .
Publishing Year
Date Published
2024-02-05
Journal Title
International Mathematics Research Notices
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.]. I 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.
ISSN
eISSN
IST-REx-ID

Cite this

Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices. 2024. doi:10.1093/imrn/rnae005
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
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.
S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,” International Mathematics Research Notices. Oxford University Press, 2024.
Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive characteristic. International Mathematics Research Notices.
Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive Characteristic.” International Mathematics Research Notices, Oxford University Press, 2024, doi:10.1093/imrn/rnae005.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data ISTA Research Explorer

Sources

arXiv 1810.12491

Search this title in

Google Scholar