7 problems.
Sheaves
- Global sections is left exact but not exact, and the exponential sequence — Hartshorne II.1.8
- The support of a section is closed, while the support of a sheaf need not be — Hartshorne II.1.14
- Stalks of the skyscraper sheaf and its description as a pushforward — Hartshorne II.1.17
Schemes
- A distinguished open of an affine scheme is the spectrum of a localization — Hartshorne II.2.1
- Reducedness on stalks and the universal property of the reduction of a scheme — Hartshorne II.2.3
- The spectrum of the integers is the terminal scheme — Hartshorne II.2.5
- Morphisms from the spectrum of a field are points with residue field inclusions — Hartshorne II.2.7