This 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.

Written 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 mathematics

Autorentext

The author taught at Brandeis University for twenty-seven years, with sabbatical time spent in Paris, Bonn, and Berkeley, and became Director of the Mathematical Sciences Research Institute in Berkeley in the Summer of 1997. At the same time he joined the faculty of UC Berkeley as Professor of Mathematics. In 2003 he became President of the American Mathematical Society. He currently serves on several editorial boards (Annals of Mathematics, Bulletin du Société Mathématique de France, Springer-Verlag's book series Algorithms and Computation in Mathematics).

Zusammenfassung
Grothendieck's beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Inhalt
Basic Definitions.- Examples.- Projective Schemes.- Classical Constructions.- Local Constructions.- Schemes and Functors.