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2. Deeper level

We have a reasonable understanding of integral models at parahoric level. Can we use new $p$-adic techniques to characterize and construct integral models at deeper level?

    1. Oort–Tate theory

          Recently Pappas–Rapoport [arXiv:2602.23245] has proposed a theory of integral models at "$\Gamma_1(p)$"-level by constructing a local model.

      Add remark

      Problem 2.1.

      [G. Pappas] Can we develop an analogue of Oort–Tate theory for the prismatic perspective? For example, what is a "$p$-divisible group with point of exact order $p$ (or even $p^n$)" from the prismatic persepective?

        • Drinfeld level structure

              We can also hope to construct integral models at $\Gamma(p)$-level.

          Add remark

          Problem 2.2.

          [E. Reinecke] Can we recast the notion of Drinfeld level structure in terms of maps of perfect complexes on the syntomification? If so, do we recover the Katz–Mazur integral model (which is not necessarily flat)?

              Cite this as: AimPL: New p-adic perspectives on canonical integral models for Shimura varieties, available at http://aimpl.org/canonicalshimura.