Class Field Theory and L Functions : Foundations and Main Results

Franz Halter-Koch

ISBN 10: 1138583588 / ISBN 13: 9781138583580

Editore: Chapman And Hall/CRC, 2022

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nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Codice articolo 9781138583580

Dati bibliografici

• Titolo: Class Field Theory and L Functions : Foundations and Main Results
• Editore: Chapman And Hall/CRC
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 1138583588
• ISBN 13: 9781138583580
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 240 L x 161 A x 36 P (millimetri) 240 millimetri di larghezza per 161 millimetri di altezza per 36 millimetri di profondità
• Peso: 1036 grammi

Descrizione articolo

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.

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).