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.
arXiv preprint arXiv:2201.06120 , year=
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For large n, mod p^n reductions of first syntomic cohomology groups of reflexive F-gauges on O_K are isomorphic iff mod p^{2n} reductions of attached Breuil-Kisin modules with G_K-action and Nygaard filtration are isomorphic.
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.
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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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Congruences of first syntomic cohomology groups
For large n, mod p^n reductions of first syntomic cohomology groups of reflexive F-gauges on O_K are isomorphic iff mod p^{2n} reductions of attached Breuil-Kisin modules with G_K-action and Nygaard filtration are isomorphic.
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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.