J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part1) - Collection des vidéos de l'Institut Fourier Accéder directement au contenu
Vidéo Année : 2017

J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part1)

Afficher 

Jean-Benoît Bost
  • Fonction : Auteur
  • PersonId : 919474
Jérémy Magnien
  • Fonction : Réalisateur
  • PersonId : 966327

Résumé

In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field k. Then the arithmetic counterpart of the dimension h0(C,V)=dimkΓ(C,V) of the space of sections of V is the non-negative real number h0θ(E,∥.∥):=log∑v∈Ee−π∥v∥2. In these lectures, I will firstly discuss diverse properties of the invariant h0θ and of its extensions to certain infinite dimensional generalizations of Euclidean lattices. Then I will present applications of this formalism to transcendence theory and to algebraization theorems in Diophantine geometry.

Dates et versions

medihal-01715959 , version 1 (23-02-2018)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

  • HAL Id : medihal-01715959 , version 1

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Jean-Benoît Bost, Jérémy Magnien. J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part1): Summer School 2017 - Arakelov Geometry and diophantine applications. 2017. ⟨medihal-01715959⟩
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