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Is there a generally accepted definition of quasifinite morphisms of Artin stacks?

It's not in the stacks project. I also checked LMB and Olsson's books but couldn't find a definition, though it's possible I didn't look hard enough.

I know if the morphism is representable then there's the obvious definition in terms of pullbacks being quasi-finite, but what about the general case?

References would be appreciated!

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A definition is given in the Stacks project (it comes from a paper by David Rydh), see Tag 0G2L.

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See

Angelo Vistoli

Intersection theory on algebraic stacks and on their moduli spaces

Inventiones mathematicae (1989)

Volume: 97, Issue: 3, page 613-670

EUDML  |  Intersection theory on algebraic stacks and on their moduli spaces.

More precisely, Definition (1.8) : the morphism is of finite type and the geometric fibers are finite, in the sense that they admit a finite atlas.

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    $\begingroup$ Hmm, strangely they don't require that a finite morphism of stacks be representable, which makes me slightly less confident that their definition of quasifinite is standard. Argh. $\endgroup$
    – stupid_question_bot
    Commented Aug 26, 2020 at 14:52
  • $\begingroup$ Also they only give the definition of a "finite type quasifinite morphism of Deligne-Mumford stacks". $\endgroup$
    – stupid_question_bot
    Commented Aug 26, 2020 at 18:31
  • $\begingroup$ not sure what you mean by 'they'. Quasi-finiteness includes of finite type already for schemes see Section 29.20 (01TC): Quasi-finite morphisms—The Stacks project . $\endgroup$
    – Niels
    Commented Aug 26, 2020 at 19:24
  • $\begingroup$ @Niels the OP is asking about Artin stacks. $\endgroup$
    – Tabes Bridges
    Commented Aug 26, 2020 at 23:30

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