ENGLISH

The Geometry of Schemes

By David Eisenbud , Joe Harris

Book information

Publisher
Springer
Year
2001
ISBN
9780387986371, 0-387-98637-5
LCC
QA564 .E357 2000
Open Library ID
OL42845M
Language
english
Format
PDF
Filesize
2 MB (1806632 bytes)
Series
Graduate texts in mathematics
Pages
297\297
Library
Springer
Time added
2009-08-06 07:02:15

Description

The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his co-workers. 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.

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