61 Pro-étale Cohomology

Section 61.1: Introduction
Section 61.2: Some topology
- Lemma 61.2.1
- Example 61.2.2
- Definition 61.2.3
- Lemma 61.2.4
- Lemma 61.2.5
Section 61.3: Local isomorphisms
- Definition 61.3.1
- Lemma 61.3.2
- Lemma 61.3.3
- Lemma 61.3.4
- Lemma 61.3.5
- Lemma 61.3.6
- Lemma 61.3.7
- Lemma 61.3.8
Section 61.4: Ind-Zariski algebra
- Definition 61.4.1
- Lemma 61.4.2
- Lemma 61.4.3
- Lemma 61.4.4
- Lemma 61.4.5
- Lemma 61.4.6
Section 61.5: Constructing w-local affine schemes
- Lemma 61.5.1
  - Equation 61.5.1.1
  - Equation 61.5.1.2
- Lemma 61.5.2
  - Equation 61.5.2.1
  - Equation 61.5.2.2
  - Equation 61.5.2.3
  - Equation 61.5.2.4
  - Equation 61.5.2.5
  - Equation 61.5.2.6
- Lemma 61.5.3
- Remark 61.5.4
- Lemma 61.5.5: Universal property of the construction
- Lemma 61.5.6
- Lemma 61.5.7
- Lemma 61.5.8
Section 61.6: Identifying local rings versus ind-Zariski
- Lemma 61.6.1
- Lemma 61.6.2
- Example 61.6.3
- Lemma 61.6.4
- Lemma 61.6.5
- Proposition 61.6.6
- Lemma 61.6.7
- Lemma 61.6.8
- Remark 61.6.9
Section 61.7: Ind-étale algebra
- Definition 61.7.1
- Lemma 61.7.2
- Lemma 61.7.3
- Lemma 61.7.4
- Lemma 61.7.5
- Lemma 61.7.6
- Lemma 61.7.7
Section 61.8: Constructing ind-étale algebras
- Lemma 61.8.1
- Remark 61.8.2
- Remark 61.8.3
- Lemma 61.8.4
- Lemma 61.8.5
- Lemma 61.8.6
- Lemma 61.8.7
Section 61.9: Weakly étale versus pro-étale
- Proposition 61.9.1
Section 61.10: The V topology and the pro-h topology
- Lemma 61.10.1
- Lemma 61.10.2
- Lemma 61.10.3
- Remark 61.10.4
Section 61.11: Constructing w-contractible covers
- Definition 61.11.1
- Lemma 61.11.2
- Proposition 61.11.3
- Remark 61.11.4
- Lemma 61.11.5
- Lemma 61.11.6
- Lemma 61.11.7
Section 61.12: The pro-étale site
- Definition 61.12.1
- Lemma 61.12.2
- Lemma 61.12.3
- Lemma 61.12.4
- Lemma 61.12.5
- Definition 61.12.6
- Definition 61.12.7
- Definition 61.12.8
- Lemma 61.12.9
- Lemma 61.12.10
- Lemma 61.12.11
- Lemma 61.12.12
- Lemma 61.12.13
- Definition 61.12.14
- Lemma 61.12.15
- Lemma 61.12.16
  - Equation 61.12.16.1
- Lemma 61.12.17
- Lemma 61.12.18
- Lemma 61.12.19
- Lemma 61.12.20
- Lemma 61.12.21
- Lemma 61.12.22
Section 61.13: Weakly contractible objects
- Lemma 61.13.1
- Lemma 61.13.2
- Lemma 61.13.3
- Lemma 61.13.4
- Lemma 61.13.5
Section 61.14: Weakly contractible hypercoverings
- Lemma 61.14.1
- Lemma 61.14.2
- Lemma 61.14.3
- Remark 61.14.4
Section 61.15: Compact generation
- Lemma 61.15.1
Section 61.16: Comparing topologies
- Lemma 61.16.1
- Lemma 61.16.2
- Lemma 61.16.3
Section 61.17: Comparing big and small topoi
- Lemma 61.17.1
- Lemma 61.17.2
- Lemma 61.17.3
- Lemma 61.17.4
Section 61.18: Points of the pro-étale site
- Lemma 61.18.1
- Lemma 61.18.2
- Lemma 61.18.3
- Lemma 61.18.4
Section 61.19: Comparison with the étale site
- Lemma 61.19.1
- Lemma 61.19.2
- Lemma 61.19.3
- Lemma 61.19.4
- Lemma 61.19.5
- Lemma 61.19.6
- Lemma 61.19.7
- Lemma 61.19.8
- Lemma 61.19.9
- Lemma 61.19.10
- Lemma 61.19.11
- Example 61.19.12
Section 61.20: Derived completion in the constant Noetherian case
- Lemma 61.20.1
- Lemma 61.20.2
Section 61.21: Derived completion and weakly contractible objects
- Proposition 61.21.1
Section 61.22: Cohomology of a point
- Lemma 61.22.1
Section 61.23: Functoriality of the pro-étale site
- Lemma 61.23.1
Section 61.24: Finite morphisms and pro-étale sites
- Lemma 61.24.1
Section 61.25: Closed immersions and pro-étale sites
- Lemma 61.25.1
- Lemma 61.25.2
- Lemma 61.25.3
- Lemma 61.25.4
- Lemma 61.25.5
- Lemma 61.25.6
Section 61.26: Extension by zero
- Definition 61.26.1
- Lemma 61.26.2
- Lemma 61.26.3
- Lemma 61.26.4
- Lemma 61.26.5
- Lemma 61.26.6
Section 61.27: Constructible sheaves on the pro-étale site
- Definition 61.27.1
- Lemma 61.27.2
- Lemma 61.27.3
- Lemma 61.27.4
- Lemma 61.27.5
- Lemma 61.27.6
Section 61.28: Constructible adic sheaves
- Definition 61.28.1
- Lemma 61.28.2
- Lemma 61.28.3
- Lemma 61.28.4
- Lemma 61.28.5
- Lemma 61.28.6
- Lemma 61.28.7
Section 61.29: A suitable derived category
- Definition 61.29.1
- Lemma 61.29.2
- Lemma 61.29.3
- Definition 61.29.4
- Lemma 61.29.5
- Lemma 61.29.6
- Proposition 61.29.7
Section 61.30: Proper base change
- Theorem 61.30.1
Section 61.31: Change of partial universe
- Lemma 61.31.1
- Lemma 61.31.2
- Lemma 61.31.3
- Lemma 61.31.4