On the average height of abelian varieties with complex multiplication

Series: 
Algebra Seminar
Monday, March 28, 2016 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
University of Chicago
,  
In the 90s, generalizing the classical Chowla-Selberg formula, P. Colmez formulated a conjectural formula for the Faltings heights of abelian varieties with multiplication by the ring of integers in a CM field, which expresses them in terms of logarithmic derivatives at 1 of certain Artin L-functions. Using ideas of Gross, he also proved his conjecture for abelian CM extensions. In this talk, I will explain a proof of Colmez's conjecture in the average for an arbitrary CM field. This is joint work with F. Andreatta, E. Goren and B. Howard.