Overview
- The present edition is a critical revision of the earlier text
- Is self-contained and well adapted for self-study
- Offers an abundance of exercises, specially adapted to the different sections
Part of the book series: Universitext (UTX)
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About this book
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. Putting forward this idea, Grothendieck revolutionized Algebraic Geometry in the late 1950s by inventing schemes. Schemes now also play an important role in Algebraic Number Theory, a field that used to be far away from Geometry. The new point of view paved the way for spectacular progress, such as the proof of Fermat's Last Theorem by Wiles and Taylor.
This book explains the scheme-theoretic approach to Algebraic Geometry for non-experts, while more advanced readers can use it to broaden their view on the subject. A separate part presents the necessary prerequisites from Commutative Algebra, thereby providing an accessible and self-contained introduction to advanced Algebraic Geometry.
Every chapter of the book is preceded by a motivating introduction with an informal discussion of its contents and background. Typical examples, and an abundance of exercises illustrate each section. Therefore the book is an excellent companion for self-studying or for complementing skills that have already been acquired. It can just as well serve as a convenient source for (reading) course material and, in any case, as supplementary literature. The present edition is a critical revision of the earlier text.
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Keywords
Table of contents (9 chapters)
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Front Matter
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Commutative Algebra
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Front Matter
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Algebraic Geometry
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Front Matter
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Back Matter
Authors and Affiliations
About the author
Prof. Dr. Siegfried Bosch, Mathematical Institute, University of Münster, Münster, Germany
Bibliographic Information
Book Title: Algebraic Geometry and Commutative Algebra
Authors: Siegfried Bosch
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-7523-0
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Ltd., part of Springer Nature 2022
Softcover ISBN: 978-1-4471-7522-3Published: 23 April 2022
eBook ISBN: 978-1-4471-7523-0Published: 22 April 2022
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 2
Number of Pages: X, 504
Number of Illustrations: 18 b/w illustrations