Intersection number of Rankin–Selberg cycles on shtukas - lecture 2 | Vidéo | Carmin.tv

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Intersection number of Rankin–Selberg cycles on shtukas - lecture 2

Appears in collection : Relative Langlands and Arithmetic - Thematic month week 5 / Langlands relatif et arithmétique - Mois thématique sem.5

The classical Rankin–Selberg integral formula (for G=GL(n) ×GL(n−1) and H=GL(n−1) ) relates integrals of Hecke eigenforms on G along H to the Rankin–Selberg L-function of the associated Galois representation. In this talk, I will present a generalization of this formula over function fields in the everywhere unramified setting, relating the self-intersection numbers of some cycles on the moduli of GShtukas to the higher derivatives of the Rankin–Selberg L-function. This can be viewed as a higher-dimensional analogue of the higher Gross–Zagier formula of Yun–Zhang. The talk will be based on my joint work with Shurui Liu.

Information about the video

Date of recording 26/02/2026
Date of publication 10/03/2026
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.20454203
Cite this video Wang, Zeyu (26/02/2026). Intersection number of Rankin–Selberg cycles on shtukas - lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20454203
URL https://dx.doi.org/10.24350/CIRM.V.20454203

Domain(s)

Number Theory

Bibliography

LIU, Shurui et WANG, Zeyu. Higher Period Integrals and Derivatives of L-functions. arXiv preprint arXiv:2504.00275, 2025 - https://doi.org/10.48550/arXiv.2504.00275
WANG, Zeyu. Special Cycle on Shtukas and Categorical Trace. arXiv preprint arXiv:2509.05526, 2025 - https://doi.org/10.48550/arXiv.2509.05526
YUN, Zhiwei et ZHANG, Wei. Shtukas and the Taylor expansion of L-functions. Annals of Mathematics, 2017, vol. 186, no 3, p. 767-911 - https://doi.org/10.4007/annals.2017.186.3.2
ARINKIN, Dima, GAITSGORY, Dennis, KAZHDAN, David, et al. The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support. arXiv preprint arXiv:2010.01906, 2020 - https://doi.org/10.48550/arXiv.2010.01906
YSENKO, Sergey. Local geometrized Rankin-Selberg method for GL (n) and its application. Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, 1999, vol. 329, no 12, p. 1065-1070 - https://doi.org/10.1016/S0764-4442(00)88475-X
FRENKEL, E., GAITSGORY, D., et VILONEN, K. On the geometric Langlands conjecture. arXiv preprint math/0012255, 2000 - https://doi.org/10.48550/arXiv.math/0012255
BRAVERMAN, Alexander, FINKELBERG, Michael, GINZBURG, Victor, et al. Mirabolic Satake equivalence and supergroups. arXiv preprint arXiv:1909.11492, 2019 - https://doi.org/10.48550/arXiv.1909.11492

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