52 Algebraic and Formal Geometry

Section 52.1: Introduction
Section 52.2: Formal sections, I
- Lemma 52.2.1
Section 52.3: Formal sections, II
- Lemma 52.3.1
- Lemma 52.3.2 reference
Section 52.4: Formal sections, III
- Lemma 52.4.1
- Lemma 52.4.2
- Lemma 52.4.3
- Lemma 52.4.4
- Lemma 52.4.5
- Example 52.4.6
Section 52.5: Mittag-Leffler conditions
- Lemma 52.5.1
- Lemma 52.5.2
- Lemma 52.5.3
- Lemma 52.5.4
Section 52.6: Derived completion on a ringed site
- Lemma 52.6.1
- Lemma 52.6.2
- Lemma 52.6.3
- Definition 52.6.4
- Lemma 52.6.5
- Lemma 52.6.6
- Lemma 52.6.7
- Lemma 52.6.8
- Lemma 52.6.9
- Lemma 52.6.10
- Lemma 52.6.11
- Proposition 52.6.12
- Remark 52.6.13: Comparison with completion
- Remark 52.6.14: Localization and derived completion
- Remark 52.6.15: Completed tensor product
- Lemma 52.6.16
- Lemma 52.6.17
- Lemma 52.6.18
- Lemma 52.6.19 reference
- Lemma 52.6.20
- Remark 52.6.21
Section 52.7: The theorem on formal functions
- Equation 52.7.0.1
- Lemma 52.7.1
- Lemma 52.7.2
- Lemma 52.7.3
- Remark 52.7.4
Section 52.8: Algebraization of local cohomology, I
- Equation 52.8.0.1
- Lemma 52.8.1
- Lemma 52.8.2
- Lemma 52.8.3
- Lemma 52.8.4
- Lemma 52.8.5
- Example 52.8.6
Section 52.9: Algebraization of local cohomology, II
- Lemma 52.9.1
- Lemma 52.9.2
- Lemma 52.9.3
- Lemma 52.9.4
- Lemma 52.9.5
Section 52.10: Algebraization of local cohomology, III
- Situation 52.10.1
- Lemma 52.10.2
- Lemma 52.10.3
- Lemma 52.10.4
- Lemma 52.10.5
- Lemma 52.10.6
- Lemma 52.10.7
- Theorem 52.10.8
- Lemma 52.10.9
Section 52.11: Algebraization of formal sections, I
- Lemma 52.11.1
- Theorem 52.11.2 reference
- Lemma 52.11.3
Section 52.12: Algebraization of formal sections, II
- Lemma 52.12.1
- Lemma 52.12.2
- Proposition 52.12.3
- Lemma 52.12.4
- Lemma 52.12.5
- Proposition 52.12.6
- Lemma 52.12.7
Section 52.13: Algebraization of formal sections, III
- Proposition 52.13.1
- Lemma 52.13.2
Section 52.14: Application to connectedness
- Lemma 52.14.1 reference
- Lemma 52.14.2
- Lemma 52.14.3
Section 52.15: The completion functor
- Lemma 52.15.1
- Lemma 52.15.2
- Lemma 52.15.3
- Lemma 52.15.4
- Lemma 52.15.5
- Lemma 52.15.6
- Lemma 52.15.7
- Lemma 52.15.8
- Lemma 52.15.9
Section 52.16: Algebraization of coherent formal modules, I
- Situation 52.16.1
- Lemma 52.16.2
  - Equation 52.16.2.1
- Lemma 52.16.3
- Example 52.16.4
- Definition 52.16.5
- Lemma 52.16.6
  - Equation 52.16.6.1
- Definition 52.16.7
- Lemma 52.16.8
- Lemma 52.16.9
- Lemma 52.16.10
- Lemma 52.16.11
- Remark 52.16.12
Section 52.17: Algebraization of coherent formal modules, II
- Lemma 52.17.1
- Lemma 52.17.2
- Lemma 52.17.3
Section 52.18: A distance function
- Equation 52.18.0.1
- Lemma 52.18.1
- Lemma 52.18.2
- Remark 52.18.3
- Example 52.18.4
Section 52.19: Algebraization of coherent formal modules, III
- Definition 52.19.1
- Lemma 52.19.2
- Lemma 52.19.3
- Lemma 52.19.4
- Lemma 52.19.5
- Lemma 52.19.6
- Lemma 52.19.7
Section 52.20: Algebraization of coherent formal modules, IV
- Lemma 52.20.1
- Remark 52.20.2
- Lemma 52.20.3
- Lemma 52.20.4
- Lemma 52.20.5
- Lemma 52.20.6
- Remark 52.20.7
Section 52.21: Improving coherent formal modules
- Lemma 52.21.1
- Lemma 52.21.2
- Lemma 52.21.3
Section 52.22: Algebraization of coherent formal modules, V
- Lemma 52.22.1
- Proposition 52.22.2: Algebraization in cohomological dimension 1 reference
- Lemma 52.22.3
  - Equation 52.22.3.1
  - Equation 52.22.3.6
- Proposition 52.22.4: Algebraization for ideals with few generators
- Lemma 52.22.5
- Remark 52.22.6
Section 52.23: Algebraization of coherent formal modules, VI
- Proposition 52.23.1
- Remark 52.23.2
- Proposition 52.23.3
- Remark 52.23.4
Section 52.24: Application to the completion functor
- Lemma 52.24.1
- Lemma 52.24.2
Section 52.25: Coherent triples
- Lemma 52.25.1
  - Equation 52.25.1.1
- Lemma 52.25.2
- Lemma 52.25.3
- Proposition 52.25.4
- Lemma 52.25.5
Section 52.26: Invertible modules on punctured spectra, I
- Lemma 52.26.1
- Proposition 52.26.2: Kollár reference
- Remark 52.26.3
Section 52.27: Invertible modules on punctured spectra, II
- Lemma 52.27.1
- Remark 52.27.2
- Lemma 52.27.3
- Lemma 52.27.4
- Lemma 52.27.5
- Proposition 52.27.6: Grothendieck
- Example 52.27.7
- Example 52.27.8
Section 52.28: Application to Lefschetz theorems
- Proposition 52.28.1
- Lemma 52.28.2
- Example 52.28.3
- Lemma 52.28.4
- Proposition 52.28.5
- Example 52.28.6
- Proposition 52.28.7