Algebraic geometry II - schemes and sheaves
MATH-510
Lecture 15 (06.11.24) summary
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Description
We covered
1) Coherent sheaves.
2) Tensor product and direct sum of quasi-coherent(resp. coherent) sheaves are quasi-cohrent (resp. coherent).
3) On affine schemes taking global section preserves the exactness of short exact sequence of quasi-coherent shaves. Failure of the analogous result in non affine case.
4) Recap of codimension.
5) Prime divisors, Weil divisors, group of divisors.
6) valuation on regular ring of dimension 1.
7) Divisor of rational function on schemes satisfying condition *.
8) Divisor class group, computation for affine spaces.
1) Coherent sheaves.
2) Tensor product and direct sum of quasi-coherent(resp. coherent) sheaves are quasi-cohrent (resp. coherent).
3) On affine schemes taking global section preserves the exactness of short exact sequence of quasi-coherent shaves. Failure of the analogous result in non affine case.
4) Recap of codimension.
5) Prime divisors, Weil divisors, group of divisors.
6) valuation on regular ring of dimension 1.
7) Divisor of rational function on schemes satisfying condition *.
8) Divisor class group, computation for affine spaces.