Lecture 14: Quasi-coherent sheaves I

We covered 13.21–13.26 and 14.1–14.12 of Gathmann's notes.

Equivalent conditions of surjectivity of morphisms of sheaves.
Tensor product of twisting sheaves (Ex 13.23)
Quasi-coherent sheaves on affine schemes: the sheaf $LaTeX: \widetilde{M}$ $\widetilde{M}$ ; homomorphisms of modules vs sheaves; compatibility with direct sums and tensor products (Lem 14.7).
Quasi-coherent sheaves on schemes.
Push-forward (along closed immersion) preserves quasi-coherence (Lem 14.8).
Closed immersions and ideal sheaves.

Suggested exercises: 13.24, 13.26, 14.11, 14.12.