Algebraic Geometry 3: Further Study of Schemes

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Title page
Contents
Contents to Volumes 1 and 2
Chapter 7. Fundamental Properties of Scheme Theory
	7.1. Algebraic Schemes and Algebraic Varieties
		a. Maximal Spectrum
		b. Algebraic Varieties
		c. Algebraic Schemes
	7.2. Dimension
		a. Krull Dimension
		b. Dimension of a Scheme
		c. Function Fields of Algebraic Varieties and Their Dimensions
		d. Normal Schemes and Regular Schemes
		e. Normalization Morphism
		f. Weil Divisors and Cartier Divisors
	7.3. Flat Morphisms and Proper Morphisms
		a. Flat Morphisms
		b. Flat Families
		c. Chow\'s Lemma and the Cohomology of Proper Morphisms
	7.4. Regular Schemes and Smooth Morphisms
		a. Kähler Differentials
		b. The Sheaf of Relative Differential Forms
		c. Regular Schemes and Non-Singular Algebraic Varietie
		d. Smooth Morphisms
	7.5. Completion and Zariski\'s Main Theorem
		a. Completion
		b. Formal Schemes and Zariski\'s Main Theorem
	Summary
	Exercises
Chapter 8. Algebraic Curves and Jacobian Varieties
	8.1. Algebraic Curves
		a. Riemann-Roch Theorem
		b. Algebraic Curves and Algebraic Function Fields
		c. Frobenius Morphisms and Étale Morphisms
	8.2. Jacobian Varieties
		a. Elliptic Curves
		b. Group Schemes
		c. Jacobian Varieties
	Summary
	Exercises
Chapter 9. Algebraic Geometry and Analytic Geometry
	9.1. Analytic Geometry
	9.2. Kodaira\'s Vanishing Theorem
	Summary
	Exercise
Overview and References
Solutions to Problems
	Chapter 7
	Chapter 8
Solutions to Exercises
	Chapter 7
	Chapter 8
	Chapter 9
Fundamental properties of scheme theory
Index
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