Puret\'e de l'approximation forte sur le corps des fonctions d'une courbe alg\'ebrique complexe

TL;DR

This paper investigates strong approximation properties over the function field of complex algebraic curves, demonstrating that certain complements of codimension 2 subsets in homogeneous spaces and smooth complete intersections satisfy strong approximation.

Contribution

It establishes new strong approximation results for complements of codimension 2 subsets in specific algebraic varieties over complex function fields.

Findings

Strong approximation holds for complements of codimension 2 subsets in homogeneous spaces.

Strong approximation applies to affine smooth complete intersections of low degree.

Results extend known approximation theorems to new classes of algebraic varieties.

Abstract

Over the function field of a complex algebraic curve, strong approximation off a non-empty finite set of places holds for the complement of a codimension $2$ closed subset in a homogeneous space under a semisimple algebraic group, and for the complement of a codimension $2$ closed subset in an affine smooth complete intersection of low degree.