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Drinfeld modules

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Drinfeld modulesby Mihran Papikian.
作者:	Papikian, Mihran.
出版者:	Cham :Springer International Publishing :2023.
面頁冊數:	xxi, 526 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Drinfeld modules.
電子資源:	https://doi.org/10.1007/978-3-031-19707-9
ISBN:	9783031197079$q(electronic bk.)

Drinfeld modules
Papikian, Mihran.

Drinfeld modules[electronic resource] /by Mihran Papikian. - Cham :Springer International Publishing :2023. - xxi, 526 p. :ill., digital ;24 cm. - Graduate texts in mathematics,v. 2962197-5612 ;. - Graduate texts in mathematics ;129..

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.

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.

ISBN: 9783031197079$q(electronic bk.)

Standard No.: 10.1007/978-3-031-19707-9doiSubjects--Topical Terms:

466780
Drinfeld modules.

LC Class. No.: QA247.3

Dewey Class. No.: 512.42

Drinfeld modules
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505 0 $a 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.
520 $a 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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