Deligne-Mumford stack

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- Tags: - #higher-algebra/stacks - Refs: - #todo/add-references - Links: - #todo/create-links

Deligne-Mumford stack

Obstruction to being a DM stack: containing a point whose automorphisms are not etale? Does not obstruct being an Artin stack though. An example involving the modular curve:

attachments/Pasted%20image%2020220807162237.png

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2022-05-25

DM stack

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quasi-smooth

Deligne-Mumford stack
Artin stack

Can prove Artin stacks are Deligne-Mumford stacks using an unramified diagonal argument.

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