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arXiv · 2206.13194

$\mathcal{G}$-$\mu$-displays and local shtuka

Sebastian Bartling
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Abstract

Two approaches to the construction of integral models of local Shimura-varieties are compared: that of B\"ultel-Pappas using $\mathcal{G}$-$\mu$-displays and that of Scholze using local mixed-characteristic shtuka. As an application, the representability of the diamond of the generic fiber of the B\"ultel-Pappas moduli problem is verified and a local representability conjecture of Rapoport-Pappas is proven. The methods apply to all unramified local Shimura-data under a certain condition on slopes and if $p\neq 2;$ thus in particular also to exceptional groups.

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Sebastian Bartling. 2022-06-27. $\mathcal{G}$-$\mu$-displays and local shtuka. https://arxiv.org/abs/2206.13194

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