Pour une d\'efinition commune des courbes elliptiques et modules de Drinfeld
Abstract
It is often stated that the Carlitz module is to the ring of univariate polynomials over a finite field what the multiplicative group is to the ring of integers. This analogy extends to the "rank 2" case, where Drinfeld modules play a role similar to that of elliptic curves. This work grew out with the will of finding a common definition for these objects, depending only on the ring of coefficients, and thus elevating this analogy to a common theory. To that end, we introduce a class of algebraic -modules for a finitely generated Dedekind ring , called "modules \'el\'ementaires", which naturally generalize Drinfeld modules, forms of the multiplicative group, and elliptic curves over a field (when has the corresponding form). The objective of this text is the classification of these "modules \'el\'ementaires".
Keywords
Cite
@article{arxiv.2306.13160,
title = {Pour une d\'efinition commune des courbes elliptiques et modules de Drinfeld},
author = {Quentin Gazda and Damien Junger},
journal= {arXiv preprint arXiv:2306.13160},
year = {2023}
}
Comments
21 pages, in French