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On the Harris-Venkatesh conjecture for weight one forms

组织者

刁晗生 , 胡悦科 , 埃马纽埃尔·勒库图里耶 , 凯撒·鲁普

演讲者

埃马纽埃尔·勒库图里耶

时间

2023年03月20日 10:00 至 11:00

地点

JCY-3

摘要

Venkatesh recently made very general conjectures regarding the relation between derived Hecke operators and a ``hidden'' action of a motivic cohomology group for an adjoint motive. These conjectures are in the setting of the cohomology of arithmetic groups. Venkatesh and Harris made an analogous conjecture in the setting of coherent cohomology in the first non-trivial case: weight one cuspidal eigenforms. This conjecture has been proved in some dihedral cases by Darmon-Harris-Rotger-Venkatesh recently. I found another approach using triple product L-functions. After some introduction on the conjecture, I will try to explain some ideas behind my method.