The Geometry of Schemes [Hardcover]

Grothendiecks beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

1 Basic Definitions 2 Examples 3 Projective Schemes 4 Classical Constructions 5 Local Constructions 6 Schemes and Functors A great subject and expert authors!
Nieuw Archief voor Wiskunde,June 2001

Both Eisenbud and Harris are experienced and compelling educators of modern mathematics. This book is strongly recommended to anyone who would like to know what schemes are all about.
Newsletter of the New Zealand Mathematical Society, No. 82, August 2001Written by two highly respected mathematicians who are also bestselling Springer authors
Fills the gap between books on classical algebraic geometry and full-blown accounts of the theory of schemes
Provides a simple account, emphasizing and explaining the universal geometric concepts behind the definitions
Explicit calculations show how scheme theory is utilized in practice
Discusses applications to number theory, physics, and applied mathematicsThis text is intended to fill the gap between texts on classical algebraic geometry and the full-blown accounts of the theory of schemes. The text focuses on interesting examples, with a minimum of machinery, to show what is happening in the field. Included is a large number of exercises, spread throughout the text. The prerequisites for reading this book are modest: a little commutative algebra and an acquaintance with algebraic varieties.