2001/03/28 by Antoine Chambert-Loir, Chambert-Loir, Antoine
Computer Science · Mathematics · #11J #14G40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Polynomial and algebraic computation #math.AG #math.NT #msc:11J #msc:14G40
paper · pdf · doi:10.48550/arxiv.math/0103192
Séminaire Bourbaki, 53e année, exp. 886, mars 2001. To appear in Asterisque
openalex publication_date 2001/03/28 · arxiv created 2002/11/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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''.