
A Syntomic Perspective on Integral Canonical Models
Alex Youcis, a mathematician at the University of Toronto, presents work with Madapusi on canonical integral models of Shimura varieties, delivered at the Institute for Advanced Study's workshop on Hodge theory and o-minimality. Youcis traces the fifty-year effort since Langlands's original program to pin down what 'canonical' should mean for these models, then proposes a new formulation built on recent p-adic Hodge theory due to Bhatt-Scholze, Drinfeld, and Bhatt-Lurie. He constructs models for pre-abelian type Shimura varieties at primes p greater than 2, extending Kisin's earlier abelian-type results, and shows how the same framework recovers results of Bakker-Shankar-Tsimerman for large primes. The talk closes on applications: Neron-type mapping properties and the question of which p-divisible groups over the algebraic closure of a finite field arise from abelian varieties. Dense, blackboard-level number theory aimed at specialists already fluent in Shimura varieties and p-adic Hodge theory.