Algebraic Geometry and Commutative Algebra

  • Siegfried Bosch

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-X
  2. Commutative Algebra

    1. Front Matter
      Pages 1-5
    2. Siegfried Bosch
      Pages 7-54
    3. Siegfried Bosch
      Pages 55-82
    4. Siegfried Bosch
      Pages 83-102
    5. Siegfried Bosch
      Pages 103-156
    6. Siegfried Bosch
      Pages 157-192
  3. Algebraic Geometry

    1. Front Matter
      Pages 193-199
    2. Siegfried Bosch
      Pages 201-276
    3. Siegfried Bosch
      Pages 277-339
    4. Siegfried Bosch
      Pages 341-397
    5. Siegfried Bosch
      Pages 399-483
  4. Back Matter
    Pages 485-504

About this book

Introduction

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.

Keywords

Hilbert’s Nullstellensatz Homological Algebra Noetherian and Artinian rings Schemes Sheaves

Authors and affiliations

  • Siegfried Bosch
    • 1
  1. 1.Mathematisches InstitutWestfälische Wilhelms-UniversitätMünsterGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-4829-6
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-4828-9
  • Online ISBN 978-1-4471-4829-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book