It can just as well serve as a convenient source for (reading) course material and, in any case, as supplementary literature. Therefore the book is an excellent companion for self-studying or for complementing skills that have already been acquired. Typical examples, and an abundance of exercises illustrate each section. A separate part presents the necessary prerequisites from Commutative Algebra, thereby providing an accessible and self-contained introduction to advanced Algebraic Geometry.Įvery chapter of the book is preceded by a motivating introduction with an informal discussion of its contents and background. 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. The new point of view paved the way for spectacular progress, such as the proof of Fermat's Last Theorem by Wiles and Taylor. Schemes now also play an important role in Algebraic Number Theory, a field that used to be far away from Geometry. Use the posttest to help you identify which topics you may need to review again. Use the pretest to identify the top-ics in which you need improvement. The tests are made up of only algebra and geometry questions. Putting forward this idea, Grothendieck revolutionized Algebraic Geometry in the late 1950s by inventing schemes. This book is divided into an algebra section and a geometry section,each comprised of eight chapters,plus a pretest and a posttest. It transcends the limited scope of pure Algebra by means of geometric construction principles. Algebraic Geometry is a fascinating branch of Mathematics that combines methods from both Algebra and Geometry.

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