Sur la torsion de la distribution ordinaire universelle attach\'ee \`a un corps de nombres

TL;DR

This paper investigates the torsion subgroup of the universal ordinary distribution associated with a general number field, providing a method to analyze and control it, with specific examples in imaginary quadratic fields.

Contribution

It introduces a new approach to control the torsion subgroup of the universal ordinary distribution for general number fields, including explicit examples for imaginary quadratic fields.

Findings

Torsion subgroups can be non-trivial in certain imaginary quadratic fields.

A method to describe and control the torsion subgroup is developed.

Examples demonstrate the existence of non-trivial torsion in specific cases.

Abstract

We study the torsion subgroup of the universal ordinary distribution related to a general number field. We describe a way to control this subgroup. We apply this method to the special case of an imaginary quadratic field, and we give examples of such fields where these torsion subgroups are non-trivial.