BOSTAN, Alin; CARUSO, Xavier; ROQUES, Julien

Metadatos

Licencia de uso del documento

BOSTAN, Alin
Calcul formel, mathématiques expérimentales et interactions [MATHEXP]

CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]

ROQUES, Julien
Institut Camille Jordan [ICJ]
Combinatoire, théorie des nombres [CTN]

Idioma

Document de travail - Pré-publication

Este ítem está publicado en

2023-04-11

Resumen en inglés

Given a linear differential equation with coefficients in $\mathbb{Q}(x)$, an important question is to know whether its full space of solutions consists of algebraic functions, or at least if one of its specific solutions is algebraic.After presenting motivating examples coming from various branches of mathematics, we advertise in an elementary way a beautiful local-global arithmetic approach to these questions, initiated by Grothendieck in the late sixties.This approach has deep ramifications and leads to the still unsolved Grothendieck-Katz $p$-curvature conjecture.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190563

Proyecto ANR

Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
Décider l'irrationalité et la transcendance - ANR-19-CE40-0018
Algorithmes Efficaces pour Guessing, Inégalités, Sommation - ANR-22-CE91-0007

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251