Modern number theory, according to Hecke, dates from Gauss's quadratic reciprocity law. The various extensions of this law and the generalizations of the domains of study for number theory have led to a rich network of ideas, which has had effects throughout mathematics, in particular in algebra. This volume of the Encyclopaedia presents the main structures and results of algebraic number theory with emphasis on algebraic number fields and class field theory. Koch has written for the non-specialist. He assumes that the reader has a general understanding of modern algebra and elementary number theory. Mostly only the general properties of algebraic number fields and related structures are included. Special results appear only as examples which illustrate general features of the theory. A part of algebraic number theory serves as a basic science for other parts of mathematics, such as arithmetic algebraic geometry and the theory of modular forms. For this reason, the chapters on basic number theory, class field theory and Galois cohomology contain more detail than the others. This book is suitable for graduate students and research mathematicians who wish to become acquainted with the main ideas and methods of algebraic number theory.

Number Theory, (Pure and Applied Mathematics, Volume 20)

Science & Math

Z.I. Borevich

I. R Shafarevich

Mathematics

Academic Press

Text: English, Russian (translation)

Basic Algebraic Geometry (Grundlehren der mathematischen Wissenschaften 217). REVISED PRINTING

Springer, Verlag

Volume 1: Varieties in Projective Space is an introduction to the theory of algebraic varieties in projective space. Paper. DLC: Geometry - Algebraic.

Basic Algebraic Geometry I

Volume 2: Schemes and Complex Manifolds, covers generalizations in two different directions of the affine and projective varieties that form the material for the first volume. Discusses the origins of algebraic geometry. Paper. DLC: Geometry - Algebraic.

Basic Algebraic Geometry 2

Springer

See the best price to sell, buy, or rent books by I. R Shafarevich. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by I. R Shafarevich

See the best price to sell, buy, or rent books by I. R Shafarevich. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Number Theory, (Pure and Applied Mathematics, Volume 20)

Basic Algebraic Geometry (Grundlehren der mathematischen Wissenschaften 217). REVISED PRINTING

Basic Algebraic Geometry I

Basic Algebraic Geometry 2