Overview
- 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
Part of the book series: Graduate Texts in Mathematics (GTM, volume 296)
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Table of contents (7 chapters)
Keywords
About this book
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.
Authors and Affiliations
About the author
Mihran Papikian received his Ph.D. from the University of Michigan in 2003. After a post-doctoral position at Stanford University, he joined the Mathematics Department of the Pennsylvania State University as a tenure-track assistant professor in 2007, becoming full professor in 2020. His research interests lie in arithmetic geometry and number theory, with an emphasis on the theory of Drinfeld modules, modular varieties, and elliptic curves. He has taught graduate courses in algebra, number theory, and various specialized topics, including Drinfeld modules.
Bibliographic Information
Book Title: Drinfeld Modules
Authors: Mihran Papikian
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-031-19707-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-19706-2Published: 01 April 2023
Softcover ISBN: 978-3-031-19709-3Published: 02 April 2024
eBook ISBN: 978-3-031-19707-9Published: 31 March 2023
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XXI, 526
Number of Illustrations: 1 b/w illustrations
Topics: Number Theory, Algebra, Algebraic Geometry