41 Étale Morphisms of Schemes

Section 41.1: Introduction
Section 41.2: Conventions
Section 41.3: Unramified morphisms
- Definition 41.3.1
- Lemma 41.3.2 slogan
- Lemma 41.3.3
- Lemma 41.3.4
- Definition 41.3.5
- Lemma 41.3.6
Section 41.4: Three other characterizations of unramified morphisms
- Theorem 41.4.1
Section 41.5: The functorial characterization of unramified morphisms
- Theorem 41.5.1
Section 41.6: Topological properties of unramified morphisms
- Proposition 41.6.1
- Theorem 41.6.2
- Proposition 41.6.3
- Lemma 41.6.4
Section 41.7: Universally injective, unramified morphisms
- Lemma 41.7.1
- Lemma 41.7.2
- Lemma 41.7.3
Section 41.8: Examples of unramified morphisms
- Example 41.8.1
- Example 41.8.2
- Example 41.8.3
Section 41.9: Flat morphisms
- Definition 41.9.1
- Theorem 41.9.2
- Definition 41.9.3
Section 41.10: Topological properties of flat morphisms
- Theorem 41.10.1
- Theorem 41.10.2
- Theorem 41.10.3
Section 41.11: Étale morphisms
- Definition 41.11.1
- Lemma 41.11.2
- Lemma 41.11.3
- Definition 41.11.4
- Lemma 41.11.5
Section 41.12: The structure theorem
- Theorem 41.12.1
- Theorem 41.12.2
- Theorem 41.12.3
Section 41.13: Étale and smooth morphisms
- Theorem 41.13.1
Section 41.14: Topological properties of étale morphisms
- Theorem 41.14.1
- Lemma 41.14.2
- Lemma 41.14.3
Section 41.15: Topological invariance of the étale topology
- Theorem 41.15.1
- Theorem 41.15.2: Une equivalence remarquable de catégories reference
Section 41.16: The functorial characterization
- Theorem 41.16.1
Section 41.17: Étale local structure of unramified morphisms
- Lemma 41.17.1
- Lemma 41.17.2
- Lemma 41.17.3
Section 41.18: Étale local structure of étale morphisms
- Lemma 41.18.1
- Lemma 41.18.2
- Lemma 41.18.3
Section 41.19: Permanence properties
- Lemma 41.19.1
- Proposition 41.19.2
- Proposition 41.19.3 slogan
- Proposition 41.19.4
- Proposition 41.19.5
- Remark 41.19.6
- Proposition 41.19.7 reference
Section 41.20: Descending étale morphisms
- Equation 41.20.0.1
- Lemma 41.20.1
- Lemma 41.20.2
- Lemma 41.20.3
- Lemma 41.20.4
- Lemma 41.20.5
- Proposition 41.20.6
Section 41.21: Normal crossings divisors
- Definition 41.21.1
- Lemma 41.21.2
- Lemma 41.21.3 slogan
- Definition 41.21.4
- Lemma 41.21.5 slogan
- Lemma 41.21.6
- Lemma 41.21.7