The Geometry of Schemes

Produktbeschreibung

The theory of schemes is the foundation for algebraic geometry proposed
and elaborated by Alexander Grothendieck and his coworkers. It has allowed
major progress in classical areas of algebraic geometry such as invariant
theory and the moduli of curves. It integrates algebraic number theory
with algebraic geometry, fulfilling the dreams of earlier generations of
number theorists. This integration has led to proofs of some of the major
conjectures in number theory (Deligne's proof of the Weil Conjectures,
Faltings proof of the Mordell Conjecture). This book is intended to bridge
the chasm between a first course in classical algebraic geometry and a
technical treatise on schemes. It focuses on examples, and strives to show
"what is going on" behind the definitions. There are many exercises to
test and extend the reader's understanding. The prerequisites are modest:
a little commutative algebra and an acquaintance with algebraic varieties,
roughly at the level of a one-semester course. The book aims to show schemes
in relation to other geometric ideas, such as the theory of manifolds.
Some familiarity with these ideas is helpful, though not required. 

Inhaltsverzeichnis

From the contents:
- I Basic Definitions
- II Examples
- III Projective Schemes
- IV Classical Constructions
- V Local Constructions
- VI Schemes and Functors
- References
- Index 

Kritik

"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 2001