Algebraic geometry and commutative algebra

Abstract

Algebraic geometry is a fascinating branch of mathematics that combinesmethods from both algebra and geometry. It transcends the limitedscope of pure algebra by means of geometric construction principles.Moreover, Grothendieck's schemes invented in the late 1950s allowedthe application of algebraic-geometric methods in fields that formerlyseemed to be far away from geometry (algebraic number theory, forexample). The new techniques paved the way to spectacular progresssuch as the proof of Fermat's Last Theorem by Wiles and Taylor.The scheme-theoretic approach to algebraic geometry is explained fornon-experts whilst more advanced readers can use the book to broadentheir view on the subject. A separate part studies the necessaryprerequisites from commutative algebra. The book provides an accessibleand self-contained introduction to algebraic geometry, up to an advancedlevel.Every chapter of the book is preceded by a motivating introductionwith an informal discussion of the contents. Typical examples andan abundance of exercises illustrate each section. Therefore thebook is an excellent solution for learning by yourself or for complementingknowledge that is already present. It can equally be used as a convenientsource for courses and seminars or as supplemental literature.