Applications of geometric invariant theory to diophantine geometry
type: Distribution
access URL: https://theses.hal.science/tel-00805516
format: HTML
issued: 2026-05-12T00:37:52.564851
modified: 2026-05-12T00:37:52.529467

test_moissonnage_selune
type: Agent

Applications of geometric invariant theory to diophantine geometry
type: Dataset
contact point: Organization
  fn: CCSD
keyword: theorie-de-kempf-ness
keyword: kempf-ness-theory
keyword: geometric-invariant-theory
keyword: theses
keyword: theorie-geometrique-des-invariants
keyword: diophantine-approximation
keyword: arakelov-geometry
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: geometrie-darakelov
keyword: approximation-diophantienne
landing page: https://theses.hal.science/tel-00805516
description: Geometric invariant theory is a central subject in nowadays' algebraic geometry : developed by Mumford in the early sixties, it enhanced the knowledge of projective varieties through the construction of moduli spaces. During the last twenty years, interactions between geometric invariant theory and arithmetic geometric --- more precisely, height theory and Arakelov geometry --- have been exploited by several authors (Burnol, Bost, Zhang, Soulé, Gasbarri, Chen). In this thesis we firstly study in a systematic way how geometric invariant theory fits in the framework of Arakelov geometry; then we show that these results give a new geometric approach to questions in diophantine approximation, proving Roth's Theorem and its recent generalizations by Lang, Wirsing and Vojta.
identifier: NNT: 2012PA112331
issued: 2026-05-12T00:37:52.549155
language: fr
modified: 2026-05-12T00:37:52.549160