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Artin's axioms, composition and moduli spaces

Jason Michael Starr
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Abstract

We prove Artin's axioms satisfy a compatibility for composition of 1-morphisms of stacks in groupoids. Consequently, some natural stacks in groupoids are algebraic, including a common generalization of Vistoli's Hilbert stack and the stack of branchvarieties of Alexeev and Knutson.

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Jason Michael Starr. 2006-02-28. Artin's axioms, composition and moduli spaces. https://arxiv.org/abs/math/0602646

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