Th\'eorie Quasicristalline des Nombres: Recherche d'une Th\'eorie de Drinfeld-Hayes en Charact\'eristique Z\'ero

TL;DR

This paper develops a framework for a Drinfeld-Hayes type theory in characteristic zero by utilizing the arithmetic of quasicrystal rings associated with number fields.

Contribution

It introduces the necessary structural foundation to extend Drinfeld-Hayes theory to characteristic zero using quasicrystal ring arithmetic.

Findings

Established a structural basis for quasicrystal rings in number fields.

Formulated a version of Drinfeld-Hayes theory in characteristic zero.

Connected quasicrystal ring arithmetic with number field properties.

Abstract

This article develops the structure necessary for the formulation of a version of Drinfeld-Hayes theory in characteristic zero, using the arithmetic of quasicrystal rings attached to a number field. -- -- Cet article d\'eveloppe la structure n\'ecessaire \`a la formulation d'une version de la th\'eorie de Drinfeld-Hayes en caract\'eristique nulle, en utilisant la th\'eorie li\'ee \`a l'arithm\'etique des anneaux quasicristallins attach\'es aux corps de nombres.