76 Groupoids in Algebraic Spaces

Section 76.1: Introduction
Section 76.2: Conventions
Section 76.3: Notation
Section 76.4: Equivalence relations
- Definition 76.4.1
- Lemma 76.4.2
- Definition 76.4.3
- Lemma 76.4.4
Section 76.5: Group algebraic spaces
- Definition 76.5.1
- Lemma 76.5.2
Section 76.6: Properties of group algebraic spaces
- Lemma 76.6.1
- Lemma 76.6.2
- Lemma 76.6.3
Section 76.7: Examples of group algebraic spaces
- Example 76.7.1: Multiplicative group algebraic space
- Example 76.7.2: Roots of unity as a group algebraic space
- Example 76.7.3: Additive group algebraic space
- Example 76.7.4: General linear group algebraic space
- Example 76.7.5
- Example 76.7.6: Constant group algebraic space
Section 76.8: Actions of group algebraic spaces
- Definition 76.8.1
  - Equation 76.8.1.1
- Definition 76.8.2
- Lemma 76.8.3
Section 76.9: Principal homogeneous spaces
- Definition 76.9.1
- Lemma 76.9.2
- Definition 76.9.3
- Lemma 76.9.4
- Lemma 76.9.5
Section 76.10: Equivariant quasi-coherent sheaves
- Definition 76.10.1
- Lemma 76.10.2
Section 76.11: Groupoids in algebraic spaces
- Definition 76.11.1
- Lemma 76.11.2
- Lemma 76.11.3
- Lemma 76.11.4
- Lemma 76.11.5
  - Equation 76.11.5.1
- Lemma 76.11.6
Section 76.12: Quasi-coherent sheaves on groupoids
- Definition 76.12.1
- Lemma 76.12.2
- Lemma 76.12.3
- Lemma 76.12.4
- Lemma 76.12.5
Section 76.13: Crystals in quasi-coherent sheaves
- Lemma 76.13.1
- Lemma 76.13.2
Section 76.14: Groupoids and group spaces
- Lemma 76.14.1
- Lemma 76.14.2
Section 76.15: The stabilizer group algebraic space
- Lemma 76.15.1
- Definition 76.15.2
- Lemma 76.15.3
Section 76.16: Restricting groupoids
- Lemma 76.16.1
- Definition 76.16.2
- Lemma 76.16.3
Section 76.17: Invariant subspaces
- Definition 76.17.1
- Lemma 76.17.2
Section 76.18: Quotient sheaves
- Equation 76.18.0.1
- Definition 76.18.1
- Remark 76.18.2
- Definition 76.18.3
- Lemma 76.18.4
- Lemma 76.18.5
- Lemma 76.18.6
- Lemma 76.18.7
Section 76.19: Quotient stacks
- Equation 76.19.0.1
- Definition 76.19.1
- Lemma 76.19.2
- Lemma 76.19.3
- Remark 76.19.4
Section 76.20: Functoriality of quotient stacks
- Lemma 76.20.1
- Lemma 76.20.2
Section 76.21: The 2-cartesian square of a quotient stack
- Lemma 76.21.1
- Lemma 76.21.2
- Lemma 76.21.3
Section 76.22: The 2-coequalizer property of a quotient stack
- Lemma 76.22.1
- Lemma 76.22.2
Section 76.23: Explicit description of quotient stacks
- Lemma 76.23.1
Section 76.24: Restriction and quotient stacks
- Lemma 76.24.1
- Lemma 76.24.2
- Lemma 76.24.3
Section 76.25: Inertia and quotient stacks
- Lemma 76.25.1
- Lemma 76.25.2
Section 76.26: Gerbes and quotient stacks
- Lemma 76.26.1
- Lemma 76.26.2
Section 76.27: Quotient stacks and change of big site
- Lemma 76.27.1
Section 76.28: Separation conditions
- Lemma 76.28.1
- Lemma 76.28.2