English
Counting $l$-adic local systems over a curve over a finite field
Multi angle
Auteurs : Yu, Hongjie (Auteur de la Conférence)
CIRM (Editeur )
11R39 - Langlands-Weil conjectures, nonabelian class field theory
14H60 - Vector bundles on curves and their moduli
22E55 - Representations of Lie and linear algebraic groups over global fields and adèle rings
CIRM (Editeur )
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Résumé :
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.
Keywords : $l$-adic local systems; automorphic representations; Higgs bundles
Codes MSC : Keywords : $l$-adic local systems; automorphic representations; Higgs bundles
11R39 - Langlands-Weil conjectures, nonabelian class field theory
14H60 - Vector bundles on curves and their moduli
22E55 - Representations of Lie and linear algebraic groups over global fields and adèle rings
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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de publication : 12/10/2023 Date de captation : 19/09/2023 Sous collection : Research talks Domaine : Number Theory Format : MP4 (.mp4) - HD Durée : 01:10:52 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-09-20_Yu.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Automorphic forms, endoscopy and trace formulas / Formes automorphes, endoscopie et formule des tracesOrganisateurs de la rencontre : Beuzart-Plessis, Raphaël ; Lemaire, Bertrand ; Nicole, Marc-Hubert ; Nyssen, Louise Dates : 18/09/2023 - 22/09/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2903.html
Données de citation
DOI : 10.24350/CIRM.V.20094403Citer cette vidéo: Yu, Hongjie (2023). Counting $l$-adic local systems over a curve over a finite field. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20094403 URI : http://dx.doi.org/10.24350/CIRM.V.20094403 |
Voir aussi
- [Multi angle] Zeta functions of Shimura varieties: past, present, and the near future / Auteur de la Conférence Zhu, Yihang.
- [Multi angle] Hecke algebras for p-adic groups, the explicit Local Langlands Correspondence and stability / Auteur de la Conférence Xu, Yujie.
- [Multi angle] Counting non-tempered automorphic forms using endoscopy / Auteur de la Conférence Gerbelli-Gauthier, Mathilde.
- [Multi angle] Motives and automorphic representations / Auteur de la Conférence Arthur, James.
Bibliographie
- 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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