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Results tagged with sheaf-theory
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user 310
For questions about sheaves on a topological space.
7
votes
When does the sheaf direct image functor f_* have a right adjoint?
Provided that $X$ is quasi-compact and separated and $f$ is separated then what is true is that $Rf_\ast \colon \operatorname{D}(X) \to \operatorname{D}(Y)$ has a right adjoint $f^!$ where these are t …
- 1,161
5
votes
Assumptions on the category C for sheafification of C-valued presheaves
To answer the first question provided one has, as you say, (small) products and equalizers the notion of sheaf makes sense as one has the right diagram corresponding to any cover. But we can just say …
- 24.1k
7
votes
Stalks of sheaf-hom
The result in Hartshorne if I recall correctly only really uses the fact that affine locally a coherent sheaf on a scheme has a locally free resolution by finite rank projectives and that one can comp …
- 8,681