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.

� propos de l?auteur:

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).

Les informations fournies dans la section � A propos du livre � peuvent faire r�f�rence � une autre �dition de ce titre.

Description de la librairie

Kennys.ie is the largest exporter of books from Ireland currently exporting to approximately 100 countries around the world. Kennys Bookshop houses hundreds of thousands of books and specialises in collection development and library services, supplying booksellers and state and university libraries on a global scale including the U.S.A.,Japan and Europe. Kennys.ie is Ireland's Largest Online Bookshop.

Visitez la page d�accueil du vendeur