Théorèmes d'algébrisation en géométrie diophantienne (Algebricity theorems in diophantine geometry)

Abstract

In a recent paper, J.-B. Bost establishes a criterion for certain ``formal subvarieties'' of algebraic varieties to be algebraic. His theorem unifies and generalizes results of Chudnovsky's and Y. André, motivated by an arithmetic conjecture of Grothendieck that predicts that the solutions of certain differential equations are algebraic functions. The proof makes use of the diophantine approximation techniques introduced by these authors but with a systematic geometric point of view, notably via Arakelov geometry and the formalism of ``slopes''.