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Study The Geometry of Schemes (Graduate Texts in Mathematics, v. 197)

Posted on 2010-03-16




Name:Study The Geometry of Schemes (Graduate Texts in Mathematics, v. 197)
ASIN/ISBN:0387986383
Language:English
File size:1.7 Mb
Language: English
Publish Date: 2000-01-01
ISBN: 0387986383
Pages: 294 pages
File Type: PDF
File Size: 1,7 MB
Other Info: Springer
   Study The Geometry of Schemes (Graduate Texts in Mathematics, v. 197)

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David Eisenbud, Joe Harris "The Geometry of Schemes (Graduate Texts in Mathematics, v. 197)"

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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