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The Geometry of Schemes
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Binding: Paperback
Dewey Decimal Number: 516.35
EAN: 9780387986371
ISBN: 0387986375
Label: Springer
Manufacturer: Springer
Number Of Items: 1
Number Of Pages: 312
Publication Date: November 29, 2001
Publisher: Springer
Studio: Springer
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Editorial Review:
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.
Customer Reviews
Average Rating: 
Rating:  - Supplement
This book is a strategic step in my campaign to be able to read EGA. Namely, I bought "The Geometry of Schemes" in order to get a better intuition for schemes (which, sadly, Hartshorne failed to provide). So far so good. There are pictures and the Eisenbud clarity I so like. I still don't get schemes, but since I haven't really read too much of the text that is to be expected.
Rating: - good for a diffrent point of few.
I like the book in a way he explains the connection between alg. geom. and com. algebra. So, if you're quiet good in on of those both theories (this is ness. for this book), then it is a good book to learn more about the other side. To be good means you had at least one good course.
It's more or less a student book (4 year or further on) to get a better few to the connection of alg geom with com algebra.
Rating:  - Crystal clear overview of a traditionally abstract subject
The theory of schemes is usually thought to be highly abstract and esoteric, and one that makes the study of algebraic geometry even more difficult. The authors definitely dispel this notion in this book, which could have been called "A Concrete Introduction to Schemes", because of the clarity with which the concepts are introduced and explained. After studying this book, one will understand and appreciate the power of schemes in algebraic geometry. The authors do an even better job than ... Read More
Rating: - A very good start
This book is clear, well written, and has a nice balance of generalities and examples. If you know the basics of rings and modules, this book will show you what schemes are and why they are useful for several different problems: for example, number theory, or studying singularities. I find it a helpful companion to Hartshorne's ALGEBRAIC GEOMETRY. But this book does not get to cohomology, and so cannot actually get to the working methods in the subject. For that, you need Hartshorne.
Rating: - Very good book
Very good book for scheme theoritical approach to Algebraic Geometry
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