Algebraic Geometry and Commutative Algebra

Algebraic Geometry is a branch of mathematics that combines algebra and geometry, and was revolutionized by Grothendieck in the late 1950s with the invention of schemes. This book provides an accessible introduction to the scheme-theoretic approach to Algebraic Geometry for non-experts, with a separate part presenting the necessary prerequisites from Commutative Algebra. Each chapter is preceded by a motivating introduction and is accompanied by examples and exercises.

Format: Paperback / softback
Length: 504 pages
Publication date: 23 April 2022
Publisher: Springer London Ltd

Algebraic Geometry is a captivating branch of Mathematics that seamlessly blends techniques from both Algebra and Geometry, expanding its scope beyond pure Algebra. By employing geometric construction principles, it transcends the confines of traditional algebraic equations. In the late 1950s, Grothendieck revolutionized Algebraic Geometry by introducing schemes, which have since become crucial in Algebraic Number Theory, a field once considered distant from Geometry. This groundbreaking perspective paved the way for remarkable advancements, including the proof of Fermat's Last Theorem by Wiles and Taylor.

This book serves as a comprehensive introduction to Algebraic Geometry for non-experts, while more advanced readers can utilize it to deepen their understanding of the subject. A separate section provides the necessary prerequisites from Commutative Algebra, offering an accessible and self-contained gateway to advanced Algebraic Geometry. Each chapter is preceded by a motivating introduction, featuring an informal discussion of its contents and background. Numerous examples and extensive exercises accompany each section, making the book an invaluable companion for self-study, as well as for complementing existing skills. It can equally serve as a convenient source for course material and supplementary literature.

This critical revision of the previous edition ensures that the content remains up-to-date and comprehensive, making it an essential resource for anyone interested in exploring the world of Algebraic Geometry.

Weight: 783g
Dimension: 235 x 155 (mm)
ISBN-13: 9781447175223
Edition number: 2nd ed. 2022