A uniform construction of stacks BT^{G,μ}_n using stacky prismatic technology verifies Drinfeld's algebraicity conjecture and yields a linear-algebraic classification of truncated p-divisible groups over general p-adic bases.
The prismatization of p-adic formal schemes
7 Pith papers cite this work. Polarity classification is still indexing.
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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-Oort strata, and central leaves.
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.
Defines prismatic cohomology relative to δ-rings, proves independence from prism structure, and establishes equivalence of three definitions under syntomicity hypotheses.
Introduces the Frobenius-Witt cotangent complex and proves it detects regularity of noetherian local rings via explicit computations on perfectoid rings.
Prismatic F-gauges are described for finite flat height one group schemes, yielding the crystalline Dieudonné module of Berthelot-Breen-Messing and flat cohomology results via Hoobler-type sequences.
Equivalence of reflexive sheaves on syntomic stack X^Syn with Z_p-lattices in crystalline local systems on generic fiber X_η, plus results on etale realization and filtered F-isocrystals for proper smooth X.
citing papers explorer
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An algebraicity conjecture of Drinfeld and the moduli of $p$-divisible groups
A uniform construction of stacks BT^{G,μ}_n using stacky prismatic technology verifies Drinfeld's algebraicity conjecture and yields a linear-algebraic classification of truncated p-divisible groups over general p-adic bases.
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On canonicity for integral models of Shimura varieties with hyperspecial level
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-Oort strata, and central leaves.
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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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Prismatic cohomology relative to $\delta$-rings
Defines prismatic cohomology relative to δ-rings, proves independence from prism structure, and establishes equivalence of three definitions under syntomicity hypotheses.
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Frobenius--Witt cotangent complexes
Introduces the Frobenius-Witt cotangent complex and proves it detects regularity of noetherian local rings via explicit computations on perfectoid rings.
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Height 1 Group Schemes and Prismatic F-Gauges
Prismatic F-gauges are described for finite flat height one group schemes, yielding the crystalline Dieudonné module of Berthelot-Breen-Messing and flat cohomology results via Hoobler-type sequences.
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Syntomification and crystalline local systems
Equivalence of reflexive sheaves on syntomic stack X^Syn with Z_p-lattices in crystalline local systems on generic fiber X_η, plus results on etale realization and filtered F-isocrystals for proper smooth X.