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Results tagged with stacks
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user 3927
In mathematics a stack or 2-sheaf is a sheaf that takes values in categories rather than sets.
13
votes
Accepted
What can we do with a coarse moduli space that we can't do with a DM moduli stack?
Note that in the above, there is no mention of DM stacks, but they come up in the proof! … I'm sure there are numerous places where coarse spaces are convenient to do some other kinds of reduction steps in proofs of general theorems, such as reducing a problem for certain DM stacks to the case …
- 7,108
35
votes
Moduli stack of principally polarized abelian varieties
The method is really the same as what Deligne-Mumford do to handle the moduli space of curves (creating a smooth cover from a part of a Hilbert scheme), except facts about curves (e.g., Riemann-Roch a …
- 7,108
38
votes
Accepted
fpqc covers of stacks
It is false. I'm not sure what the comment about algebraic spaces has to do with the question, since algebraic spaces do admit an fpqc (even \'etale) cover by a scheme. This is analogous to the fact …
- 7,108