Drinfeld Modules (Graduate Texts in Mathematics, 296, Band 296) - Hardcover

Buch 178 von 180: Graduate Texts in Mathematics

Papikian, Mihran

 
9783031197062: Drinfeld Modules (Graduate Texts in Mathematics, 296, Band 296)
Hardcover
ISBN 10: 3031197062 ISBN 13: 9783031197062
Verlag: Springer, 2023

Inhaltsangabe

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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Über die Autorin bzw. den Autor

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.




Von der hinteren Coverseite

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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Verlag
Springer
Erscheinungsdatum
2023
Sprache
Englisch
ISBN 10 
3031197062
ISBN 13 
9783031197062
Einband
Gebundene Ausgabe
Anzahl der Seiten
547
Kontakt zum Hersteller
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Deutschland

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