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A brief introduction to Drinfeld modules. (English) Zbl 0793.11015
Goss, David (ed.) et al., The arithmetic of function fields. Proceedings of the workshop at the Ohio State University, June 17-26, 1991, Columbus, Ohio (USA). Berlin: Walter de Gruyter. Ohio State Univ. Math. Res. Inst. Publ. 2, 1-32 (1992).
As the title indicates, the paper gives an introduction to the theory of Drinfeld modules. In the first part, some motivation is presented from calculations (due to Carlitz) on factorials and exponential functions related to \(A= \mathbb{F}_ r[T]\), and from Stark’s conjectures. Having introduced the basic definitions (Drinfeld modules over fields, twists by ideals of the base ring \(A\), rank, height, Tate module), the analytic construction of Drinfeld modules is given, which resembles the Weierstraß construction of elliptic curves over \(\mathbb{C}\) through their period lattices. In the second part, the author focusses on rank one Drinfeld modules, their fields of definition, and their relation to (abelian) class field theory of the underlying global function field \(K\).
The paper is highly recommended as a compact and effective introduction to the subject. It contains many references and hints that will lead the interested reader to more far-reaching but less accessible articles.
For the entire collection see [Zbl 0771.00031].

MSC:
11G09 Drinfel’d modules; higher-dimensional motives, etc.
11-02 Research exposition (monographs, survey articles) pertaining to number theory
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