Drinfeld Modules

Beschreibung

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 conveniently recalling 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
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 conveniently recalling 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.


Offers an accessible introduction to Drinfeld modules Features a hands-on, "computational" style, containing numerous exercises Provides a self-contained, high-quality reference for researchers

Autor*in

Mihran Papikian

Themen in »Drinfeld Modules«

Drinfield modules Function field arithmetic Finite fields and linearized polynomials Non-archimedean analysis Reciprocity laws

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“This is an excellent textbook suitable for graduate courses and for the self-study of novices, but also for experienced mathematicians who want to enter the field. I bet it will become the canonical reference in the field.” (Ernst-Ulrich Gekeler, Mathematical Reviews, May, 2024)

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