Elements of Algebraic Geometry

IV. Local study of schemes and morphisms of schemes — Part four

A. Grothendieck (with the collaboration of J. Dieudonné).

Publications mathématiques de l'IHÉS, tome 32 (1967), pp. 5–361. numdam.org/item?id=PMIHES_1967__32__5_0

© Publications mathématiques de l'I.H.É.S., 1967.

Chapter IV (continued)

Local study of schemes and morphisms of schemes

This fourth and final part of Chapter IV develops the differential and étale theory of morphisms: differential invariants and differentially smooth morphisms (§16); smooth, unramified, and étale morphisms (§17); complements on étale morphisms and Henselian local rings (§18); regular and transversally regular immersions (§19); meromorphic functions and pseudo-morphisms (§20); and divisors (§21).

Sommaire (Chapter IV, conclusion)

• §16. Differential invariants. Differentially smooth morphisms.
• §17. Smooth, unramified, étale morphisms.
• §18. Complements on étale morphisms. Henselian local rings.
• §19. Regular and transversally regular immersions.
• §20. Meromorphic functions; pseudo-morphisms.
• §21. Divisors.

Translator's note. The 1964 sommaire announced §§20 and 21 as "Hyperplane sections; generic projections" and "Infinitesimal extensions" respectively. In Part 4 (1967) the program was revised: §20 became Meromorphic functions; pseudo-morphisms and §21 became Divisors. The translation files use the published §20 and §21 titles.