Cours/Séminaire
Notice
Langue :
Anglais
Crédits
Jérémy MAGNIEN (Réalisation), Gérard Freixas i Montplet (Intervention)
Conditions d'utilisation
CC BY-NC-ND 4.0
DOI : 10.60527/kc5j-8k17
Citer cette ressource :
Gérard Freixas i Montplet. I_Fourier. (2017, 28 juin). G. Freixas i Montplet - Automorphic forms and arithmetic intersections (part 2) , in 2017. [Vidéo]. Canal-U. https://doi.org/10.60527/kc5j-8k17. (Consultée le 16 juillet 2024)

# G. Freixas i Montplet - Automorphic forms and arithmetic intersections (part 2)

Réalisation : 28 juin 2017 - Mise en ligne : 16 mars 2018
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Descriptif

In these lectures I will focus on the Riemann-Roch theorem in Arakelov geometry, in the specific context of some simple Shimura varieties. For suitable data, the cohomological part of the theorem affords an interpretation in terms of both holomorphic and non-holomorphic modular forms. The formula relates these to arithmetic intersection numbers, that can sometimes be evaluated through variants of the first Kroenecker limit formula. I will first explain these facts, and then show how the Jacquet-Langlands correspondence allows to relate arithmetic intersection numbers for different Shimura varieties, whose associated groups are closely related.

Intervention
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