Drinfeld Modules, Modular Schemes and Applications

By: GEEL J VAN

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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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Preface
Introduction to Drinfeld Modules	p. 3
Moduli Schemes of Drinfeld Modules	p. 17
Analytic Theory of Drinfeld Modules	p. 32
A Guide to Explicit Class Field Theory in Global Function Fields	p. 44
Drinfeld Modules Over Finite Fields	p. 66
Some Rigid Geometry	p. 88
The Structure of [Omega] and Its Quotients [Lambda]/[Omega]	p. 103
Analytic Compactification and Modular Forms	p. 113
Algebraic Compactification and Modular Interpretation	p. 141
A Survey of Drinfeld Modular Form	p. 167
Automorphic Forms and Drinfeld's Reciprocity Law	p. 188
Jacquet-Langlands Theory Over K and Relations With Elliptic Curves	p. 224
On Hilbert Class Field Towers of Global Function Fields	p. 261
Drinfeld Modular Forms of Level T	p. 272
Explicit Reciprocity Law for a Rank One Drinfeld F[subscript q][t]-Module	p. 282
Groups of Elliptic Units and Torsion Points of Drinfeld Modules	p. 298
L-Series of Automorphic Cusp Forms of Drinfeld Type	p. 311
Hyperelliptic Drinfeld Modular Curves	p. 330
Local Height Pairings of Heegner Points on Drinfeld Curves	p. 344
List of Participants	p. 357
Table of Contents provided by Blackwell. All Rights Reserved.

Drinfeld Modules, Modular Schemes and Applications

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Hardcover

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