On an algebro-geometric approach to the automatic convergence theorem for Shimura varieties
Haocheng Fan (BICMR – Peking University)

In the first part of this talk, I will provide an upper bound for the coherent cohomological dimension of the Siegel modular variety, and then show that the boundary of the compactified Siegel modular variety satisfies the Grothendieck–Lefschetz condition, which implies the automatic convergence theorem in this case. In the second part, I will introduce a work in progress, joint with Peihang Wu and Jiacheng Xia, to generalize this approach to general Shimura varieties by assuming an algebraicity result on the space of symmetric formal Fourier-Jacobi series.

Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).