Class Field Theory and L Functions: Foundations and Main Results - Rilegato

Halter-Koch, Franz

Rilegato

ISBN 10: 1138583588 ISBN 13: 9781138583580

Casa editrice: Chapman and Hall/CRC, 2022

Riassunto

The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras.

While the first three chapters presuppose only basic algebraic and topological knowledge, the rest of the books assumes knowledge of the basic theory of algebraic numbers and algebraic functions, such as those contained in my previous book, An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020).

The main features of the book are:

• A detailed study of Pontrjagin’s dualtiy theorem.
• A thorough presentation of the cohomology of profinite groups.
• A introduction to simple algebras.
• An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language.
• The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse.
• The study of holomorphy domains and their relevance for class field theory.
• Simple classical proofs of the functional equation for L functions both for number fields and function fields.
• A self-contained presentation of the theorems of representation theory needed for Artin L functions.
• Application of Artin L functions for arithmetical results.

Su questo libro

Informazioni sull'autore

Franz Halter-Koch is professor emeritus at the University of Graz, Graz, Austria. He is the author of Ideal Systems (Marcel Dekker,1998), Quadratic Irrationals (CRC, 2013), co-author of Non-Unique Factorizations (CRC 2006), and An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020).

Dalla quarta di copertina

Through a set of related yet distinct texts, the author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions: Ideal- and valuation-theoretic aspects, L functions and class field theory, with a presentation of algebraic foundations which are usually undersized in standard algebra courses.

Dettagli dell'edizione

• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 1138583588
• ISBN 13: 9781138583580
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 564
• Contatto del produttore: Taylor and Francis, GPSR Taylor and Francis; gpsr@taylorandfrancis.com; ; Taylor & Francis Verlag GmbH, Kaufingerstraße 24; München; 80331; Germania