F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part3)

Fabrizio Andreatta (1) , Jérémy Magnien (2)

1 Dipartimento di Matematica "Federigo Enriques"
2 IF - Institut Fourier

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersection of such divisors and the CM points. We will show that they imply an averaged version of a conjecture of Colmez. Finally we will present the main ingredients in the proof of the conjectures. The lectures are base on joint works with E. Goren, B. Howard and K. Madapusi Pera.

Mots clés: Arakelov Geometry and diophantine applications; height; CM points; Shimura varieties; orthogonal; Colmez conjecture

Mots clés: eem2017; Géométrie d'Arakelov et applications diophantiennes; Grenoble

Domaines: Mathématiques [math]

Fabrizio Andreatta, Jérémy Magnien. F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part3): Summer School 2017 - Arakelov Geometry and diophantine applications. 2017. ⟨medihal-01669080⟩