Format:
1 Online-Ressource (XXI, 526 Seiten)
ISBN:
9783031197079
Series Statement:
Graduate Texts in Mathematics 296
Content:
Preface -- Acknowledgements -- Notation and Conventions -- Chapter 1. Algebraic Preliminaries -- Chapter 2. Non-Archimedean Fields -- Chapter 3. Basic Properties of Drinfeld Modules -- Chapter 4. Drinfeld Modules over Finite Fields -- Chapter 5. Analytic Theory of Drinfeld Modules -- Chapter 6. Drinfeld Modules over Local Fields -- Chapter 7. Drinfeld Modules over Global Fields -- Appendix A. Drinfeld modules for general function rings -- Appendix B. Notes on exercises -- Bibliography -- Index.
Content:
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.
Additional Edition:
ISBN 9783031197062
Additional Edition:
ISBN 9783031197086
Additional Edition:
ISBN 9783031197093
Additional Edition:
Erscheint auch als Druck-Ausgabe Papikian, Mihran Drinfeld modules Cham : Springer, 2023 ISBN 9783031197062
Language:
English
Keywords:
Drinfeld-Modul
;
Nichtarchimedisch geordneter Körper
;
Polynomring
;
Torsion
;
Galois-Feld
;
Lokaler Körper
;
Galois-Darstellung
DOI:
10.1007/978-3-031-19707-9
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