99 Quot and Hilbert Spaces

Section 99.1: Introduction
Section 99.2: Conventions
Section 99.3: The Hom functor
- Situation 99.3.1
  - Equation 99.3.1.1
- Lemma 99.3.2
- Lemma 99.3.3
- Remark 99.3.4
- Lemma 99.3.5
- Lemma 99.3.6
- Lemma 99.3.7
- Lemma 99.3.8
- Lemma 99.3.9
- Proposition 99.3.10
Section 99.4: The Isom functor
- Lemma 99.4.1
- Lemma 99.4.2
- Proposition 99.4.3
Section 99.5: The stack of coherent sheaves
- Situation 99.5.1
- Lemma 99.5.2
- Lemma 99.5.3
- Lemma 99.5.4
- Remark 99.5.5
- Lemma 99.5.6
- Lemma 99.5.7
- Lemma 99.5.8
- Lemma 99.5.9
- Lemma 99.5.10
- Lemma 99.5.11
- Theorem 99.5.12: Algebraicity of the stack of coherent sheaves; flat case
Section 99.6: The stack of coherent sheaves in the non-flat case
- Theorem 99.6.1: Algebraicity of the stack of coherent sheaves; general case
Section 99.7: The functor of quotients
- Situation 99.7.1
  - Equation 99.7.1.1
  - Equation 99.7.1.2
- Remark 99.7.2
- Remark 99.7.3
- Lemma 99.7.4
- Lemma 99.7.5
- Lemma 99.7.6
- Lemma 99.7.7
- Lemma 99.7.8
- Remark 99.7.9: Obstructions for quotients
- Remark 99.7.10: Deformations of quotients
Section 99.8: The Quot functor
- Situation 99.8.1
  - Equation 99.8.1.1
- Lemma 99.8.2
- Lemma 99.8.3
- Proposition 99.8.4
- Remark 99.8.5: Quot via Artin's axioms
Section 99.9: The Hilbert functor
- Situation 99.9.1
  - Equation 99.9.1.1
- Lemma 99.9.2
- Lemma 99.9.3
- Proposition 99.9.4
Section 99.10: The Picard stack
- Lemma 99.10.1
- Proposition 99.10.2
Section 99.11: The Picard functor
- Situation 99.11.1
- Lemma 99.11.2
- Lemma 99.11.3
- Lemma 99.11.4
- Lemma 99.11.5
- Lemma 99.11.6
- Lemma 99.11.7
- Proposition 99.11.8
- Lemma 99.11.9
Section 99.12: Relative morphisms
- Lemma 99.12.1
- Lemma 99.12.2
- Proposition 99.12.3
Section 99.13: The stack of algebraic spaces
- Lemma 99.13.1
- Lemma 99.13.2
- Lemma 99.13.3
- Lemma 99.13.4
- Remark 99.13.5
- Lemma 99.13.6
- Lemma 99.13.7
- Lemma 99.13.8
- Lemma 99.13.9
- Remark 99.13.10
Section 99.14: The stack of polarized proper schemes
- Situation 99.14.1
  - Equation 99.14.1.1
- Lemma 99.14.2
- Lemma 99.14.3
- Lemma 99.14.4
- Remark 99.14.5
- Lemma 99.14.6
- Lemma 99.14.7
- Lemma 99.14.8
- Lemma 99.14.9
- Lemma 99.14.10
- Lemma 99.14.11: Strong formal effectiveness for polarized schemes slogan
- Lemma 99.14.12
- Lemma 99.14.13
- Remark 99.14.14
- Theorem 99.14.15: Algebraicity of the stack of polarized schemes
Section 99.15: The stack of curves
- Situation 99.15.1
  - Equation 99.15.1.1
- Lemma 99.15.2
- Lemma 99.15.3
- Lemma 99.15.4
- Remark 99.15.5
- Lemma 99.15.6
- Lemma 99.15.7
- Lemma 99.15.8
- Lemma 99.15.9
- Lemma 99.15.10
- Theorem 99.15.11: Algebraicity of the stack of curves reference
- Lemma 99.15.12
- Remark 99.15.13
Section 99.16: Moduli of complexes on a proper morphism
- Lemma 99.16.1
- Lemma 99.16.2
- Situation 99.16.3
- Lemma 99.16.4
- Lemma 99.16.5
- Lemma 99.16.6
- Remark 99.16.7
- Lemma 99.16.8
- Lemma 99.16.9
- Lemma 99.16.10
- Lemma 99.16.11
- Theorem 99.16.12: Algebraicity of moduli of complexes on a proper morphism reference