Algebraic geometry and commutative algebra Siegfried Bosch

Format:

Book

Author/Creator:

Bosch, S. (Siegfried), 1944-

Series:

Universitext

Language:

English

Subjects (All):

Geometry, Algebraic.

Algebra.

algebra.

Physical Description:

1 online resource

Place of Publication:

London New York Springer ©2013

System Details:

text file

PDF

Summary:

Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck's schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved the way to spectacular progress such as the proof of Fermat's Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature

Contents:

Part 1. Commutative Algebra Rings and Modules The Theory of Noetherian Rings Integral Extensions Extension of Coefficients and Descent Homological Methods: Ext and Tor

Part 2. Algebraic Geometry Affine Schemes and Basic Constructions Techniques of Global Schemes Étale and Smooth Morphisms Projective Schemes and Proper Morphisms

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Bosch, S. (Siegfried), 1944- Algebraic geometry and commutative algebra

ISBN:

1447148290

9781447148296

1447148282

9781447148289

9781447175230

1447175239

OCLC:

821020969

Access Restriction:

Restricted for use by site license