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Drinfeld Modules, Modular Schemes ...

by Geel J Van

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Drinfeld modules and arithmetic geometry over function fields

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AlbakiReads Editorial

Drinfeld modules and arithmetic geometry over function fields

This volume combines a 12-lecture instructional course on Drinfeld modules and their moduli spaces with research papers on related topics. Its mathematical setting is the arithmetic geometry of global function fields, where Drinfeld modules are presented through analogies with elliptic curves and abelian varieties. The course connects the study of moduli spaces with subjects including explicit class field theory, Jacquet–Langlands theory, and modular forms; the accompanying papers also address Heegner points. Together, these components offer both a structured introduction to the subject and examples of research directions developed around it.

Good fit for readers who enjoy

  • Mathematics readers studying arithmetic geometry over function fields.
  • Readers seeking an instructional treatment of Drinfeld modules alongside related research papers.
  • Researchers interested in connections among moduli spaces, class field theory, modular forms, and Heegner points.

Themes

Drinfeld modulesArithmetic geometry of global function fieldsModuli spacesClass field theoryModular forms and Heegner points

Based on publisher information and book metadata.

Book overview

In his 1974 seminal paper "Elliptic modules", V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as "Drinfeld Modules". They have many beautiful analogies with elliptic curves and abelian varieties. They study of their moduli spaces leads amongst others to explicit class field theory, Jacquet-Langlands theory, and a proof of the Shimura-Taniyama-Weil conjecture for global function fields.

This book constitutes a carefully written instructional course of 12 lectures on these subjects, including many recent novel insights and examples. The instructional part is complemented by research papers centering around class field theory, modular forms and Heegner points in the theory of global function fields.

The book will be indispensable for everyone who wants a clear view of Drinfeld's original work, and wants to be informed about the present state of research in the theory of arithmetic geometry over function fields.

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