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Drinfeld Modules
Buch von Mihran Papikian
Sprache: Englisch

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Beschreibung
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.
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.
Über 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.

Zusammenfassung

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

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2023
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: xxi
526 S.
1 s/w Illustr.
526 p. 1 illus.
ISBN-13: 9783031197062
ISBN-10: 3031197062
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Papikian, Mihran
Hersteller: Springer Nature Switzerland
Springer International Publishing
Springer International Publishing AG
Graduate Texts in Mathematics
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 35 mm
Von/Mit: Mihran Papikian
Erscheinungsdatum: 01.04.2023
Gewicht: 0,98 kg
Artikel-ID: 124668857
Über 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.

Zusammenfassung

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

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2023
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: xxi
526 S.
1 s/w Illustr.
526 p. 1 illus.
ISBN-13: 9783031197062
ISBN-10: 3031197062
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Papikian, Mihran
Hersteller: Springer Nature Switzerland
Springer International Publishing
Springer International Publishing AG
Graduate Texts in Mathematics
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 35 mm
Von/Mit: Mihran Papikian
Erscheinungsdatum: 01.04.2023
Gewicht: 0,98 kg
Artikel-ID: 124668857
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