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<p>We establish a representability criterion of <i>v</i>-sheaf theoretic modifications of formal schemes and apply this criterion to moduli spaces of parahoric level structures on local shtukas. In the proof, we introduce nice classes of equivariant profinite perfectoid covers and study geometric quotients of perfectoid formal schemes by profinite groups. As a corollary, we show the local representability of integral models of local Shimura varieties under hyperspecial levels, and study the forgetful morphisms between integral models of Shimura varieties associated with inclusions of parahoric subgroups under hyperspecial levels.</p>

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Relative representability and parahoric level structures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月11日

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  • Yuta Takaya

摘要

We establish a representability criterion of v-sheaf theoretic modifications of formal schemes and apply this criterion to moduli spaces of parahoric level structures on local shtukas. In the proof, we introduce nice classes of equivariant profinite perfectoid covers and study geometric quotients of perfectoid formal schemes by profinite groups. As a corollary, we show the local representability of integral models of local Shimura varieties under hyperspecial levels, and study the forgetful morphisms between integral models of Shimura varieties associated with inclusions of parahoric subgroups under hyperspecial levels.