Introduction To Algebraic Geometry And Commutative Algebra
This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.
1100250549
Introduction To Algebraic Geometry And Commutative Algebra
This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.
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Introduction To Algebraic Geometry And Commutative Algebra

Introduction To Algebraic Geometry And Commutative Algebra

by Dilip P Patil, Uwe Storch
Introduction To Algebraic Geometry And Commutative Algebra

Introduction To Algebraic Geometry And Commutative Algebra

by Dilip P Patil, Uwe Storch

Hardcover

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Overview

This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.

Product Details

ISBN-13: 9789814304566
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 04/01/2010
Series: Iisc Lecture Notes Series , #1
Pages: 220
Product dimensions: 6.20(w) x 9.00(h) x 0.80(d)

Table of Contents

Series Preface v

Preface vii

Chapter 1 Finitely Generated Algebras

1.A Algebras over a Ring 1

1.B Factorization in Rings 2

1.C Noetherian Rings and Modules 4

1.D Graded Rings and Modules 7

1.E Integral Extensions 8

1.F Noether's Normalization Lemma and Its Consequences 12

Chapter 2 The K-Spectrum and the Zariski Topology

2.A The K-Spectrum of a K-Algebra 19

2.B Affine Algebraic Sets 21

2.C Strong Topology 32

Chapter 3 Prime Spectra and Dimension

3.A The Prime Spectrum of a Commutative Ring 41

3.B Dimension 48

Chapter 4 Schemes

4.A Sheaves of Rings 61

4.B Schemes 68

4.C Finiteness Conditions on Schemes 75

4.D Product of Schemes 77

4.E Affine Morphisms 83

Chapter 5 Projective Schemes

5.A Projective Schemes 87

5.B Main Theorem of Elimination 102

5.C Mapping Theorem of Chevalley 107

Chapter 6 Regular, Normal and Smooth Points

6.A Regular Local Rings 111

6.B Normal Domains 118

6.C Normalization of a Scheme 125

6.D The Module of Kähler Differentials 128

6.E Quasi-coherent Sheaves and the Sheaf of Kähler Differentials 139

Chapter 7 Riemann-Roch Theorem

7.A Coherent Modules on Projective Schemes 153

7.B Projective Curves 158

7.C The Projective Line 163

7.D Riemann-Roch Theorem for General Curves 167

7.E Genus of a Projective Curve 175

References 199

List of Symbols 201

Index 203

Biography of Authors 209

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