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Results tagged with ag.algebraic-geometry
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user 322
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
22
votes
Accepted
Functorial characterization of open subschemes?
The abelian category of quasicoherent sheaves on a schemes determine the scheme. This is an old result of Gabriel ("des categories abeliennes" 1962), proved in full generality by Rosenberg. This means …
12
votes
Bimodules in geometry
The Fourier-Mukai transform comes from a bimodule: the Poincaré bundle. Let $A$ be an abelian variety, the Poincaré bundle $\mathcal{P}$ is a vector bundle on $A \times \hat{A}$ coming from the fact t …
11
votes
Accepted
Non-zero sheaf cohomology
The sheaf cohomology ${H}^i(X,F)$ of a (topological) manifold $X$ of dimension $n$ vanishes for $i > n$. This is a topological version of Grothendieck's vanishing theorem above. You can find this resu …