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Synopsis
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.
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Review
"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
Synopsis
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.
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The Geometry of Schemes
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Springer-Verlag New York Inc., 2000
ISBN 10: 0387986375
ISBN 13: 9780387986371
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The Geometry of Schemes
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ISBN 10: 0387986375
ISBN 13: 9780387986371
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Grothendieck's 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. 312 pp. Englisch. Seller Inventory # 9780387986371
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The Geometry of Schemes (Graduate Texts in Mathematics, Band 197).
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New York. Springer-Verlag., 2000
ISBN 10: 0387986375
ISBN 13: 9780387986371
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kartoniert. Condition: Sehr gut. Zust: Gutes Exemplar. 294 Seiten, mit Abbildungen, Englisch 438g. Seller Inventory # 494221
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