Algebraic geometry II - schemes and sheaves

MATH-510

Lecture 26 (13.12.23) Summary

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1) Every quasicoehrent sheaf on a noetherian scheme can be embedded inside a quasicoherent flasque sheaf.
2) Derived pushforward.
3) Flasque sheaves are acyclic with respect to the pushforward functor.
4) Derived pushforward of quasicoherent sheaves from a noetherian scheme are quasicoherent.
5) Derived pushforward computes usual sheaf cohomology when then target is affine.
6) Vanishing of derived pushforwards.
7) Cech complex of sheaves and groups, Cech cohomology, example.
8) Cech cohomology of a quasi-coherent sheaf on a noetherian scheme concides with the sheaf cohomology.