C. Soulé - Arithmetic Intersection (Part1)

Christophe Soulé (1) , Jérémy Magnien (2)

1 IHES - Institut des Hautes Études Scientifiques
2 IF - Institut Fourier

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic intersection number of ¯L and ¯M. We shall explain the definition and the basic properties of this number. Next, we shall see how to extend this construction to higher dimension, and how to interpret it in terms of arithmetic Chow groups.

Mots clés: Arakelov Geometry and diophantine applications; arithmetic; intersection

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

Domaines: Mathématiques [math]

Christophe Soulé, Jérémy Magnien. C. Soulé - Arithmetic Intersection (Part1): Summer School 2017 - Arakelov Geometry and diophantine applications. 2017. ⟨medihal-01720026⟩