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Relative representability and parahoric level structures
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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.
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Cited by 4 Pith papers
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A correspondence is shown between lim-perfectoid splitting of projective schemes and lim-perfectoid purity of their Gorenstein section rings, supplying new examples of lim-perfectoid pure rings.
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New aperture-based definition and construction of integral canonical models for pre-abelian and exceptional Shimura varieties at hyperspecial level, with uniform proofs of non-emptiness for all Newton strata, Ekedahl-...
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Algebraization of absolute perfectoidization via section rings
A graded absolute perfectoidization is built for G-graded adic rings, with the key result that the absolute perfectoidization of the structure sheaf on projective-type formal schemes algebraizes.
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A local-global correspondence for perfectoid purity
A correspondence links lim-perfectoid splitting of projective schemes to lim-perfectoid purity of their Gorenstein section rings, supplying new examples of lim-perfectoid pure rings beyond complete intersections and s...
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