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  • Textbook
  • May 2023

Drinfeld Modules

Authors:

  1. Mihran Papikian

    1. Department of Mathematics, Pennsylvania State University, University Park, USA

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  • 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)

Hardcover Book USD 109.99
Price excludes VAT (USA)
This title has not yet been released. You may pre-order it now and we will ship your order when it is published on 16 May 2023.
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About this book

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.


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Keywords

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

  • Department of Mathematics, Pennsylvania State University, University Park, USA

    Mihran Papikian

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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.




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Bibliographic Information

  • Book Title: Drinfeld Modules

  • Authors: Mihran Papikian

  • Series Title: Graduate Texts in Mathematics

  • 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: 978-3-031-19706-2Due: 16 May 2023

  • Softcover ISBN: 978-3-031-19709-3Due: 16 May 2024

  • eBook ISBN: 978-3-031-19707-9Due: 16 May 2023

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XXI, 532

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Number Theory, Algebra, Algebraic Geometry

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Hardcover Book USD 109.99
Price excludes VAT (USA)
This title has not yet been released. You may pre-order it now and we will ship your order when it is published on 16 May 2023.
Learn about institutional subscriptions