Crystalline Galois representations acquire mu_p-equivariant Breuil-Kisin module reductions, yielding the ↑ constraint on inertial weights and proving weight elimination for a general Serre weight conjecture.
The prismatization of p-adic formal schemes
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this note, we introduce and study the Cartier--Witt stack $\mathrm{WCart}_X$ attached to a $p$-adic formal scheme $X$ as well as some variants. In particular, we reinterpret the notion of prismatic crystals on $X$ and their cohomology in terms of quasicoherent sheaf theory on $\mathrm{WCart}_X$ in favorable situations.
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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.
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.
Defines prismatic cohomology relative to δ-rings, proves independence from prism structure, and establishes equivalence of three definitions under syntomicity hypotheses.
Defines the Frobenius-Witt cotangent complex and establishes its link to regularity of noetherian local rings as a derived form of Saito's criterion, using 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.
Graded absolute perfectoidization of G-graded adic rings yields an algebraization of the structure sheaf of projective-type formal schemes.
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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Reduction modulo p of crystalline Galois representations via {\mu}_p-equivariance
Crystalline Galois representations acquire mu_p-equivariant Breuil-Kisin module reductions, yielding the ↑ constraint on inertial weights and proving weight elimination for a general Serre weight conjecture.
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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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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
Defines the Frobenius-Witt cotangent complex and establishes its link to regularity of noetherian local rings as a derived form of Saito's criterion, using 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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Algebraization of absolute perfectoidization via section rings
Graded absolute perfectoidization of G-graded adic rings yields an algebraization of the structure sheaf of projective-type formal schemes.
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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.