Lecture 13: Sheaves of modules

We covered 13.1–13.20 of Gathmann's notes.

• Presheaves and sheaves of O_X-modules.
• Free sheaves, direct sums. Direct image sheaf. Skyscraper sheaf.
• Twisting sheaves on Pⁿ.
• Morphisms of sheaves. Kernel sheaf, image presheaf, coker presheaf, quotient presheaf, tensor presheaf.
• Sheafification. Image sheaf, coker sheaf, quotient sheaf, tensor sheaf.

Suggested exercises: 13.6, 13.8 (iso of sheaves local), 13.18 (univ prop of sheafification!), 13.20.