Axiomatic definition establishes unique, functorial Igusa stacks for Shimura data, highlighting implications.
We provide an axiomatic definition of an Igusa stack associated to an arbitrary Shimura datum. We then prove that Igusa stacks are unique and automatically functorial with respect to morphisms of Shimura data, assuming their existence. Using the same techniques, we also prove that the existence of the Igusa stack passes to a Shimura subdatum.
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Dongryul Kim (2025) studied this question.
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