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For questions about sheaves on a topological space.

4 votes
0 answers
138 views

Examples of non-hypercomplete sheaves on affine schemes

Let $A$ be a commutative ring and let $\mathcal{O}$ be a sheaf of $E_{\infty}$-ring spectra on $\mathrm{Spec} A$ such that $\pi_0\mathcal{O} = \mathcal{O}_{\mathrm{Spec} A}$. Lurie provides a criterio …
Lennart Meier's user avatar
8 votes

relation between sheaf of hom and hom of sheaf

Just to give a few more details on Daniel's comments: In general, $\mathcal{H}om_{\mathcal{O}_X}(\mathcal{M},\mathcal{N})$ is not the associated sheaf to $Hom_A(M,N)$. Simple example: Take $A = \math …
Lennart Meier's user avatar
7 votes
3 answers
2k views

Are the global sections of a vector bundle a projective module?

Given a scheme $X$ with structure sheaf $\mathcal{O}_X$, we can associate to each $\mathcal{O}_X$-module $\mathcal{F}$ its global sections $\Gamma(\mathcal{F})$, which gets the structure of a $\Gamma( …
Lennart Meier's user avatar
3 votes

What books should I read before beginning Masaki Kashiwara and Pierre Schapira's "Sheaves on...

I think, the first volume of Harder's Lectures on Algebraic Geometry contains a nice and balanced account of sheaf theory and the cohomology of sheaves. Besides the title, it is not really a book abou …