The notion of display, which was introduced by Zink, has been successfully applied to the deformation theory of p-divisible groups. Recently, for a reductive group G over the ring of p-adic integers, Lau introduced the notion of G-display. In this talk, following the approach of Lau, we study displays and G-displays over the prismatic site of Bhatt-Scholze. In particular, we explain the deformation theory for such G-displays.
We also discuss two applications: a conjecture of Pappas-Rapoport on the local representability of integral local Shimura varieties, and an alternative proof of the classification of p-divisible groups over a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, which was previously obtained by Kisin for odd p and by Kim, Lau, and Liu for p=2.

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