1. Local structures🔗

This chapter serves for the first half of the commutative algebra preparation of the remaining part of the paper. The key result is Theorem 1.8.5, expressing that for any ring A, there exists an ind-étale faithfully flat A-algebra D with D w-contractible. That is to say, every affine scheme has a w-contractible cover in the "pro-(étale site)".

1. 1.1. Preliminaries
2. 1.2. ind-Zariski maps
3. 1.3. Henselian objects and Henselisation
4. 1.4. Ind-étale ring maps
5. 1.5. w-local spaces
6. 1.6. w-local rings
7. 1.7. w-strictly-local rings
8. 1.8. w-contractible rings