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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
4
votes
Accepted
Removable base loci for non-projective varieties
Short answer: No.
In his original paper, Fujita posed the question whether we can weaken the assumptions in the theorem. (Fujita 1983, 1.16) There has been one paper written since then with an attemp …
3
votes
Accepted
componentwise injective quasi coherent sheaves
The condition you want is $X$ a locally noetherian scheme. Then by Hartshorne's "Residues & Dualities," Proposition 7.17, $\cal{F}$ is an injective ${\cal O}_X$-module if and only if for each $x \in X …
5
votes
learning crystalline cohomology
If you don't mind reading mimeographed notes, the exposition by Berthelot and Ogus is certainly worth taking a look at. It has the added advantage of only assuming a minimal background in algebra and …