The Stacks project

Table of contents

• Part 1: Preliminaries
  • Chapter 1: Introduction

    pdf
  • Chapter 2: Conventions

    pdf
  • Chapter 3: Set Theory

    pdf
  • Chapter 4: Categories

    pdf
  • Chapter 5: Topology

    pdf
  • Chapter 6: Sheaves on Spaces

    pdf
  • Chapter 7: Sites and Sheaves

    pdf
  • Chapter 8: Stacks

    pdf
  • Chapter 9: Fields

    pdf
  • Chapter 10: Commutative Algebra

    pdf
  • Chapter 11: Brauer groups

    pdf
  • Chapter 12: Homological Algebra

    pdf
  • Chapter 13: Derived Categories

    pdf
  • Chapter 14: Simplicial Methods

    pdf
  • Chapter 15: More on Algebra

    pdf
  • Chapter 16: Smoothing Ring Maps

    pdf
  • Chapter 17: Sheaves of Modules

    pdf
  • Chapter 18: Modules on Sites

    pdf
  • Chapter 19: Injectives

    pdf
  • Chapter 20: Cohomology of Sheaves

    pdf
  • Chapter 21: Cohomology on Sites

    pdf
  • Chapter 22: Differential Graded Algebra

    pdf
  • Chapter 23: Divided Power Algebra

    pdf
  • Chapter 24: Differential Graded Sheaves

    pdf
  • Chapter 25: Hypercoverings

    pdf

  ---

• Part 2: Schemes
  • Chapter 26: Schemes

    pdf
  • Chapter 27: Constructions of Schemes

    pdf
  • Chapter 28: Properties of Schemes

    pdf
  • Chapter 29: Morphisms of Schemes

    pdf
  • Chapter 30: Cohomology of Schemes

    pdf
  • Chapter 31: Divisors

    pdf
  • Chapter 32: Limits of Schemes

    pdf
  • Chapter 33: Varieties

    pdf
  • Chapter 34: Topologies on Schemes

    pdf
  • Chapter 35: Descent

    pdf
  • Chapter 36: Derived Categories of Schemes

    pdf
  • Chapter 37: More on Morphisms

    pdf
  • Chapter 38: More on Flatness

    pdf
  • Chapter 39: Groupoid Schemes

    pdf
  • Chapter 40: More on Groupoid Schemes

    pdf
  • Chapter 41: Étale Morphisms of Schemes

    pdf

  ---

• Part 3: Topics in Scheme Theory
  • Chapter 42: Chow Homology and Chern Classes

    pdf
  • Chapter 43: Intersection Theory

    pdf
  • Chapter 44: Picard Schemes of Curves

    pdf
  • Chapter 45: Weil Cohomology Theories

    pdf
  • Chapter 46: Adequate Modules

    pdf
  • Chapter 47: Dualizing Complexes

    pdf
  • Chapter 48: Duality for Schemes

    pdf
  • Chapter 49: Discriminants and Differents

    pdf
  • Chapter 50: de Rham Cohomology

    pdf
  • Chapter 51: Local Cohomology

    pdf
  • Chapter 52: Algebraic and Formal Geometry

    pdf
  • Chapter 53: Algebraic Curves

    pdf
  • Chapter 54: Resolution of Surfaces

    pdf
  • Chapter 55: Semistable Reduction

    pdf
  • Chapter 56: Functors and Morphisms

    pdf
  • Chapter 57: Derived Categories of Varieties

    pdf
  • Chapter 58: Fundamental Groups of Schemes

    pdf
  • Chapter 59: Étale Cohomology

    pdf
  • Chapter 60: Crystalline Cohomology

    pdf
  • Chapter 61: Pro-étale Cohomology

    pdf
  • Chapter 62: Relative Cycles

    pdf
  • Chapter 63: More Étale Cohomology

    pdf
  • Chapter 64: The Trace Formula

    pdf

  ---

• Part 4: Algebraic Spaces
  • Chapter 65: Algebraic Spaces

    pdf
  • Chapter 66: Properties of Algebraic Spaces

    pdf
  • Chapter 67: Morphisms of Algebraic Spaces

    pdf
  • Chapter 68: Decent Algebraic Spaces

    pdf
  • Chapter 69: Cohomology of Algebraic Spaces

    pdf
  • Chapter 70: Limits of Algebraic Spaces

    pdf
  • Chapter 71: Divisors on Algebraic Spaces

    pdf
  • Chapter 72: Algebraic Spaces over Fields

    pdf
  • Chapter 73: Topologies on Algebraic Spaces

    pdf
  • Chapter 74: Descent and Algebraic Spaces

    pdf
  • Chapter 75: Derived Categories of Spaces

    pdf
  • Chapter 76: More on Morphisms of Spaces

    pdf
  • Chapter 77: Flatness on Algebraic Spaces

    pdf
  • Chapter 78: Groupoids in Algebraic Spaces

    pdf
  • Chapter 79: More on Groupoids in Spaces

    pdf
  • Chapter 80: Bootstrap

    pdf
  • Chapter 81: Pushouts of Algebraic Spaces

    pdf

  ---

• Part 5: Topics in Geometry
  • Chapter 82: Chow Groups of Spaces

    pdf
  • Chapter 83: Quotients of Groupoids

    pdf
  • Chapter 84: More on Cohomology of Spaces

    pdf
  • Chapter 85: Simplicial Spaces

    pdf
  • Chapter 86: Duality for Spaces

    pdf
  • Chapter 87: Formal Algebraic Spaces

    pdf
  • Chapter 88: Algebraization of Formal Spaces

    pdf
  • Chapter 89: Resolution of Surfaces Revisited

    pdf

  ---

• Part 6: Deformation Theory
  • Chapter 90: Formal Deformation Theory

    pdf
  • Chapter 91: Deformation Theory

    pdf
  • Chapter 92: The Cotangent Complex

    pdf
  • Chapter 93: Deformation Problems

    pdf

  ---

• Part 7: Algebraic Stacks
  • Chapter 94: Algebraic Stacks

    pdf
  • Chapter 95: Examples of Stacks

    pdf
  • Chapter 96: Sheaves on Algebraic Stacks

    pdf
  • Chapter 97: Criteria for Representability

    pdf
  • Chapter 98: Artin's Axioms

    pdf
  • Chapter 99: Quot and Hilbert Spaces

    pdf
  • Chapter 100: Properties of Algebraic Stacks

    pdf
  • Chapter 101: Morphisms of Algebraic Stacks

    pdf
  • Chapter 102: Limits of Algebraic Stacks

    pdf
  • Chapter 103: Cohomology of Algebraic Stacks

    pdf
  • Chapter 104: Derived Categories of Stacks

    pdf
  • Chapter 105: Introducing Algebraic Stacks

    pdf
  • Chapter 106: More on Morphisms of Stacks

    pdf
  • Chapter 107: The Geometry of Algebraic Stacks

    pdf

  ---

• Part 8: Topics in Moduli Theory
  • Chapter 108: Moduli Stacks

    pdf
  • Chapter 109: Moduli of Curves

    pdf

  ---

• Part 9: Miscellany
  • Chapter 110: Examples

    pdf
  • Chapter 111: Exercises

    pdf
  • Chapter 112: A Guide to the Literature

    pdf
  • Chapter 113: Desirables

    pdf
  • Chapter 114: Coding Style

    pdf
  • Chapter 115: Obsolete

    pdf
  • Chapter 116: GNU Free Documentation License

    pdf

  ---