On canonicity for integral models of Shimura varieties with hyperspecial level

We give a new definition – and in some cases, a new construction – of integral canonical models of Shimura varieties that uses the notion of an aperture appearing in work of Gardner–Madapusi on some conjectures of Drinfeld. This applies to Shimura varieties of pre-abelian type at odd primes of hyperspecial level, recovering and extending previous work of Kisin, Kim–Madapusi and Imai–Kato–Youcis, but also to exceptional Shimura varieties for large enough primes. The characterization in the exceptional case is \emph{a priori} different from the one recently shown by Bakker–Shankar–Tsimerman, and recovers many of their results, such as the existence of prime-to-$p$ Hecke operators, the non-emptiness of the $\mu$-ordinary stratum and the theory of the canonical lift. In fact, we give a uniform proof of the non-emptiness of \emph{all} possible Newton strata, and of the non-emptiness of Ekedahl–Oort strata and central leaves as well. An important ingredient in the proofs is a generalization of Tate’s full faithfulness theorem for $p$-divisible groups to the context of apertures. This leads to a mapping property for the integral canonical model that characterizes maps into it from all normal, flat and excellent schemes over ${\mathbb{Z}}_{(p)}$.