Counting $l$-adic local systems over a curve over a finite field | Vidéo | Carmin.tv

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Counting $l$-adic local systems over a curve over a finite field

Appears in collection : Automorphic forms, endoscopy and trace formulas / Formes automorphes, endoscopie et formule des traces

In 1981, Drinfeld enumerated the number of irreducible $l$-adic local systems of rank two on a projective smooth curve fixed by the Frobenius endomorphism. Interestingly, this number looks like the number of points on a variety over a finite field. Deligne proposed conjectures to extend and comprehend Drinfeld's result. By the Langlands correspondence, it is equivalent to count certain cuspidal automorphic representations over a function field. In this talk, I will present some counting results where we connect counting to the number of stable Higgs bundles using Arthur's non-invariant trace formula.

Information about the video

Date of recording 19/09/2023
Date of publication 12/10/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20094403
Cite this video Yu, Hongjie (19/09/2023). Counting $l$-adic local systems over a curve over a finite field. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20094403
URL https://dx.doi.org/10.24350/CIRM.V.20094403

Bibliography

YU, Hongjie. Comptage des systémes locaux ℓ-adiques sur une courbe. Annals of Mathematics, 2023, vol. 197, no 2, p. 423-531. - http://dx.doi.org/10.4007/annals.2023.197.2.1
YU, Hongjie. $\ell $-adic local systems and Higgs bundles: the generic case. arXiv preprint arXiv:2304.06637, 2023. - https://doi.org/10.48550/arXiv.2304.06637
YU, Hongjie. Rank 2$\ell $-adic local systems and Higgs bundles over a curve. arXiv preprint arXiv:2301.13157, 2023. - https://doi.org/10.48550/arXiv.2301.13157

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