These are the notes for a 6 h course given by the author during the summer school “Géométrie d’Arakelov”, organized by the Institut Fourier (Grenoble) in the summer of 2017. They are based on the paper “Faltings’ Heights of Abelian Varieties with Complex Multiplication” by myself, Eyal Goren, Ben Howard and Keerthi Madapusi Pera and on notes by myself and Eyal Goren. No new results are presented. The goal is to describe the strategy to reduce the proof of an averaged version of Colmez’s conjecture to a conjecture of Bruinier, Kudla and Yang, an instance of what is known as the Kudla’s program.

The Height of CM Points on Orthogonal Shimura Varieties and Colmez’s Conjecture / F. Andreatta (LECTURE NOTES IN MATHEMATICS). - In: Arakelov Geometry and Diophantine Applications / [a cura di] E. Peyre, G. Rémond. - [s.l] : Springer, 2021. - ISBN 9783030575588. - pp. 433-462 [10.1007/978-3-030-57559-5_13]

The Height of CM Points on Orthogonal Shimura Varieties and Colmez’s Conjecture

F. Andreatta
2021

Abstract

These are the notes for a 6 h course given by the author during the summer school “Géométrie d’Arakelov”, organized by the Institut Fourier (Grenoble) in the summer of 2017. They are based on the paper “Faltings’ Heights of Abelian Varieties with Complex Multiplication” by myself, Eyal Goren, Ben Howard and Keerthi Madapusi Pera and on notes by myself and Eyal Goren. No new results are presented. The goal is to describe the strategy to reduce the proof of an averaged version of Colmez’s conjecture to a conjecture of Bruinier, Kudla and Yang, an instance of what is known as the Kudla’s program.
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/829978
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