Algebraic geometry II - schemes and sheaves

MATH-510

Content of Lecture_12.11.25

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1) Finishing proof of local freeness of Kahler differentials vs regularity.

2) Abelian categories, exact, additive functors.

3) Categories of O_X modules, quasi-coherent, coherent modules.

4) Hom sheaf, tensor product, pushforward, pullback of sheaves.

5) Description in the affine case.

6) Pushforward of a quasicoherent sheaf is quasicoherent along a quasicompact quasiseparated map.

7) Sheaves on Proj associated to a graded module.