Article thumbnail

: École d’Été 2017 - Géométrie d'Arakelov et applications diophantiennes

By Fabrizio Andreatta and Jérémy Magnien

Abstract

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

Topics: orthogonal, CM points, Shimura varieties, Colmez conjecture, height, Arakelov Geometry and diophantine applications, eem2017, Grenoble, Géométrie d'Arakelov et applications diophantiennes, [MATH]Mathematics [math]
Publisher: HAL CCSD
Year: 2017
OAI identifier: oai:HAL:medihal-01669036v1
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • https://hal.archives-ouvertes.... (external link)
  • https://hal.archives-ouvertes.... (external link)
  • https://hal.archives-ouvertes.... (external link)
  • https://hal.archives-ouvertes.... (external link)
  • https://hal.archives-ouvertes.... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.