Table of contents
-
Part 1: Preliminaries
Chapter 1: Introduction
pdfChapter 2: Conventions
pdfChapter 3: Set Theory
pdfChapter 4: Categories
pdfChapter 5: Topology
pdfChapter 6: Sheaves on Spaces
pdfChapter 7: Sites and Sheaves
pdfChapter 8: Stacks
pdfChapter 9: Fields
pdfChapter 10: Commutative Algebra
pdfChapter 11: Brauer groups
pdfChapter 12: Homological Algebra
pdfChapter 13: Derived Categories
pdfChapter 14: Simplicial Methods
pdfChapter 15: More on Algebra
pdfChapter 16: Smoothing Ring Maps
pdfChapter 17: Sheaves of Modules
pdfChapter 18: Modules on Sites
pdfChapter 19: Injectives
pdfChapter 20: Cohomology of Sheaves
pdfChapter 21: Cohomology on Sites
pdfChapter 22: Differential Graded Algebra
pdfChapter 23: Divided Power Algebra
pdfChapter 24: Differential Graded Sheaves
pdfChapter 25: Hypercoverings
pdf
-
Part 2: Schemes
Chapter 26: Schemes
pdfChapter 27: Constructions of Schemes
pdfChapter 28: Properties of Schemes
pdfChapter 29: Morphisms of Schemes
pdfChapter 30: Cohomology of Schemes
pdfChapter 31: Divisors
pdfChapter 32: Limits of Schemes
pdfChapter 33: Varieties
pdfChapter 34: Topologies on Schemes
pdfChapter 35: Descent
pdfChapter 36: Derived Categories of Schemes
pdfChapter 37: More on Morphisms
pdfChapter 38: More on Flatness
pdfChapter 39: Groupoid Schemes
pdfChapter 40: More on Groupoid Schemes
pdfChapter 41: Étale Morphisms of Schemes
pdf
-
Part 3: Topics in Scheme Theory
Chapter 42: Chow Homology and Chern Classes
pdfChapter 43: Intersection Theory
pdfChapter 44: Picard Schemes of Curves
pdfChapter 45: Weil Cohomology Theories
pdfChapter 46: Adequate Modules
pdfChapter 47: Dualizing Complexes
pdfChapter 48: Duality for Schemes
pdfChapter 49: Discriminants and Differents
pdfChapter 50: de Rham Cohomology
pdfChapter 51: Local Cohomology
pdfChapter 52: Algebraic and Formal Geometry
pdfChapter 53: Algebraic Curves
pdfChapter 54: Resolution of Surfaces
pdfChapter 55: Semistable Reduction
pdfChapter 56: Functors and Morphisms
pdfChapter 57: Derived Categories of Varieties
pdfChapter 58: Fundamental Groups of Schemes
pdfChapter 59: Étale Cohomology
pdfChapter 60: Crystalline Cohomology
pdfChapter 61: Pro-étale Cohomology
pdfChapter 62: Relative Cycles
pdfChapter 63: More Étale Cohomology
pdfChapter 64: The Trace Formula
pdf
-
Part 4: Algebraic Spaces
Chapter 65: Algebraic Spaces
pdfChapter 66: Properties of Algebraic Spaces
pdfChapter 67: Morphisms of Algebraic Spaces
pdfChapter 68: Decent Algebraic Spaces
pdfChapter 69: Cohomology of Algebraic Spaces
pdfChapter 70: Limits of Algebraic Spaces
pdfChapter 71: Divisors on Algebraic Spaces
pdfChapter 72: Algebraic Spaces over Fields
pdfChapter 73: Topologies on Algebraic Spaces
pdfChapter 74: Descent and Algebraic Spaces
pdfChapter 75: Derived Categories of Spaces
pdfChapter 76: More on Morphisms of Spaces
pdfChapter 77: Flatness on Algebraic Spaces
pdfChapter 78: Groupoids in Algebraic Spaces
pdfChapter 79: More on Groupoids in Spaces
pdfChapter 80: Bootstrap
pdfChapter 81: Pushouts of Algebraic Spaces
pdf
-
Part 5: Topics in Geometry
Chapter 82: Chow Groups of Spaces
pdfChapter 83: Quotients of Groupoids
pdfChapter 84: More on Cohomology of Spaces
pdfChapter 85: Simplicial Spaces
pdfChapter 86: Duality for Spaces
pdfChapter 87: Formal Algebraic Spaces
pdfChapter 88: Algebraization of Formal Spaces
pdfChapter 89: Resolution of Surfaces Revisited
pdf
-
Part 6: Deformation Theory
Chapter 90: Formal Deformation Theory
pdfChapter 91: Deformation Theory
pdfChapter 92: The Cotangent Complex
pdfChapter 93: Deformation Problems
pdf
-
Part 7: Algebraic Stacks
Chapter 94: Algebraic Stacks
pdfChapter 95: Examples of Stacks
pdfChapter 96: Sheaves on Algebraic Stacks
pdfChapter 97: Criteria for Representability
pdfChapter 98: Artin's Axioms
pdfChapter 99: Quot and Hilbert Spaces
pdfChapter 100: Properties of Algebraic Stacks
pdfChapter 101: Morphisms of Algebraic Stacks
pdfChapter 102: Limits of Algebraic Stacks
pdfChapter 103: Cohomology of Algebraic Stacks
pdfChapter 104: Derived Categories of Stacks
pdfChapter 105: Introducing Algebraic Stacks
pdfChapter 106: More on Morphisms of Stacks
pdfChapter 107: The Geometry of Algebraic Stacks
pdf
-
Part 8: Topics in Moduli Theory
Chapter 108: Moduli Stacks
pdfChapter 109: Moduli of Curves
pdf
-
Part 9: Miscellany
Chapter 110: Examples
pdfChapter 111: Exercises
pdfChapter 112: A Guide to the Literature
pdfChapter 113: Desirables
pdfChapter 114: Coding Style
pdfChapter 115: Obsolete
pdfChapter 116: GNU Free Documentation License
pdf