Aspects of Global Class Field Theory
by Huishi Li;G Gras GeorgesGras (9783540441335)

Aspects of Global Class Field Theory
 

Huishi Li;G Gras GeorgesGras


Release Date: 14 November 2002
Format: Hardback
Pages: 512
Category: Number Theory
Publisher: Springer
ISBN: 9783540441335
ISBN-10: 3540441336



Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idA]les, ray class fields, symbols, reciprocity laws, Hasse's principles, the Grunwald--Wang theorem, Hilbert's towers, ...). He also proves some new or less-known results (reflection theorem, structure of the abelian closure of a number field) and lays emphasis on the invariant T_p, of abelian p-ramification, which is related to important Galois cohomology properties and p-adic conjectures. This book gives much material in an elementary way, and is suitable for students, researchers, and all who are fascinated by this theory.

In the corrected 2nd printing 2005, the author improves many details all along the book (e.g., he gives an interpretation of the Spiegelungssatz for the pth cyclotomic field regarding the Kummer--Vandiver conjecture in a probabilistic point of view).

AUD $210.95

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