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- catalog abstract "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.".
- catalog contributor b11506151.
- catalog contributor b11506152.
- catalog contributor b11506153.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description "I Basic Definitions -- II Examples -- III Projective Schemes -- IV Classical Constructions -- V Local Constructions -- VI Schemes and Functors -- References -- Index.".
- catalog description "Includes bibliographical references (p. [279]-283) and index.".
- catalog description "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.".
- catalog extent "x, 294 p. :".
- catalog identifier "0387986375 (softcover : alk. paper)".
- catalog identifier "0387986383 (hardcover : alk. paper)".
- catalog isPartOf "Graduate texts in mathematics ; 197".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "516.3/5 21".
- catalog subject "Geometry, algebraic.".
- catalog subject "Mathematics.".
- catalog subject "QA564 .E357 2000".
- catalog subject "Schemes (Algebraic geometry)".
- catalog tableOfContents "I Basic Definitions -- II Examples -- III Projective Schemes -- IV Classical Constructions -- V Local Constructions -- VI Schemes and Functors -- References -- Index.".
- catalog title "The geometry of schemes / David Eisenbud, Joe Harris.".
- catalog type "text".