Drinfeld Modules

This textbook provides an introduction to Drinfeld modules, mathematical objects essential to modern number theory, with applications in various fields of arithmetic. It assumes a graduate-level understanding of abstract algebra and covers topics such as isogenies, torsion points, and number-theoretic applications. The book is designed for a graduate course and can also serve as a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields.

Format: Hardback
Length: 526 pages
Publication date: 02 March 2023
Publisher: Springer International Publishing AG

This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory.

After the first two chapters, which conveniently recall prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized.

Drinfeld Modules guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic.

Weight: 980g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031197062
Edition number: 1st ed. 2023