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Zeta functions of Shimura varieties: past, present, and the near future
Multi angle
Authors : Zhu, Yihang (Author of the conference)
CIRM (Publisher )
11G15 - Complex multiplication and moduli of abelian varieties, See also {14K22}
11G18 - Arithmetic aspects of modular and Shimura varieties
14G35 - Modular and Shimura varieties
CIRM (Publisher )
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Abstract :
I will first recall the general expectations of Shimura, Langlands, and Kottwtiz on the shape of the zeta function of a Shimura variety, or more generally its etale cohomology. I will then report on some recent progress which partially fulfills these expectations, for Shimura varieties of unitary groups and special orthogonal groups. Finally, I will give a preview of some foreseeable developments in the near future.
Keywords : Shimura varieties; Hasse-Weil zeta function
MSC Codes : Keywords : Shimura varieties; Hasse-Weil zeta function
11G15 - Complex multiplication and moduli of abelian varieties, See also {14K22}
11G18 - Arithmetic aspects of modular and Shimura varieties
14G35 - Modular and Shimura varieties
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 12/10/2023 Conference Date : 19/09/2023 Subseries : Research talks arXiv category : Number Theory ; Algebraic Geometry Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 01:01:00 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-09-19_Zhu.mp4 
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Information on the Event
Event Title : Automorphic forms, endoscopy and trace formulas / Formes automorphes, endoscopie et formule des tracesEvent Organizers : Beuzart-Plessis, Raphaël ; Lemaire, Bertrand ; Nicole, Marc-Hubert ; Nyssen, Louise Dates : 18/09/2023 - 22/09/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2903.html
Citation Data
DOI : 10.24350/CIRM.V.20094603Cite this video as: Zhu, Yihang (2023). Zeta functions of Shimura varieties: past, present, and the near future. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20094603 URI : http://dx.doi.org/10.24350/CIRM.V.20094603 |
See Also
- [Multi angle] Counting $l$-adic local systems over a curve over a finite field / Author of the conference Yu, Hongjie.
- [Multi angle] Hecke algebras for p-adic groups, the explicit Local Langlands Correspondence and stability / Author of the conference Xu, Yujie.
- [Multi angle] Counting non-tempered automorphic forms using endoscopy / Author of the conference Gerbelli-Gauthier, Mathilde.
- [Multi angle] Motives and automorphic representations / Author of the conference Arthur, James.
Bibliography
- KISIN, Mark, SHIN, Sug Woo, et ZHU, Yihang. The stable trace formula for Shimura varieties of abelian type. arXiv preprint arXiv:2110.05381, 2021. - https://doi.org/10.48550/arXiv.2110.05381
