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Drinfeld Modules: An Introduction

  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 210)

Abstract

In the last chapter we introduced a special class of Drinfeld modules for the ring A = F[T] defined over the field k = F(T) and discussed some of their properties. By considering the Carlitz module, in particular, we were able to construct a family of field extensions of k with properties remarkably similar to those of cyclotomic fields. In this chapter we will give a more general definition of a Drinfeld module. The definition and theory of these modules was given by V. Drinfeld in the mid-seventies, see Drinfeld [1, 2]. The application of the rank 1 theory to the class field theory of global function fields is due to Drinfeld and independently to D. Hayes [2]. The article by Hayes [6] provides a compact introduction to this material. A comprehensive treatment of Drinfeld modules (and, even more generally, T-modules) can be found in the treatise of Goss [4].

Keywords

Entire Function Left Ideal Newton Polygon Dedekind Domain Fractional Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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