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finally created stub for Artin stack
also rewrote and expanded the Idea-section at Deligne-Mumford stack
a few days back I had worked my old query box at algebraic stack into the definition. But hastily so.
All three of these entries (algebraic stack, Deligne-Mumford stack and Artin stack ) need careful polishing and expansion. My suggestion is that we eventually expand algebraic stack to a comprehensive discussion and have the other two be more or less clarification of terminology and otherwise be just redirects.
I should repeat again that what Lurie calls Deligne-Mumford is according to him not quite the same in details to what others call Deligne-Mumford. The entry seems to be mixing theorems/characterizations on both variants as if there were the same.
Lurie does not require separatedness.
Aha. Is this spoiling the local picture of a scheme modulo finite group (with condition on slices) quotient interpretation or not ?
P.S. people talk also of Deligne-Mumford orbifolds in differentiable settings.
I was planning today to sit down and $n$-labify the nice chapter on algebraic stacks in The Stacks Project document to clearly expose the relation between the various axioms and the notion of groupoids internal to algebraic spaces. But it seems that I won’t find the time soon.
This nice idea may be a little tricky as it may contaminate $n$Lab with various copy licences which are pretty detailed in their case.
In a differentiable setup
This nice idea may be a little tricky as it will contaminate nLab with various copy licences which are pretty detailed in their case.
Well, I read material all the time in books and papers and then write out my understanding of it on the $n$Lab. We don’t need to (and probably don’t even want to) copy material verbatim.
Good. I misunderstood the phrase :)
Robbin-Salamon is very good as it emphasises the relations between groupoid point of view and atlases and few other points of relation between concrete and abstract nonsense. Also becuase it does it in differentiable setup.
added pointer to the original:
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