Average Heights of Abelian Varieties with Complex Multiplication

Explore the intricate relationship between periods and L-functions in the context of abelian varieties with complex multiplication. Delve into Pierre Colmez's groundbreaking conjecture from the 1990s, which proposes a precise connection between periods and the degree 1 coefficient of certain Artin L-functions' Taylor expansion at 0. Learn about Colmez's proof for the cyclotomic field case and discover how recent work by Tonghai Yang, Bruinier, Kudla, and Yang has led to proving a consequence of Colmez's conjecture for average periods of abelian varieties with complex multiplication by a fixed CM number field. Gain insights into this collaborative research effort with F. Andreatta, E. Goren, and B. Howard, presented as part of the International Congress of Basic Science 2024.

Keerthi Sampath Madapusi: Average heights of abelian varieties with complex multiplication #ICBS2024