Faltings heights and subleading terms of adjoint L-functions
Ryan Chen (Princeton)

Colmez’s conjecture predicts that Faltings heights of CM abelian varieties appear in subleading terms of certain Artin L-functions. An averaged version is known by the work of Andreatta–Goren–Howard–Madapusi and Yuan–Zhang. We propose a generalized problem relating diagonal cycles on (n-1)-dimensional unitary Shimura varieties and adjoint L-functions of certain automorphic representations of U(n). The case n=1 is (a variant of) the averaged Colmez conjecture. I will explain some origins of our conjecture, discuss our predictions in the general case, and report on our results in the case in the case of n = 2, via trace formula. This is joint work in progress with Weixiao Lu and Wei Zhang.

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