A functor D_crys is constructed that links prismatic F-crystals to filtered Frobenius crystals and, in the Fontaine-Laffaille range, induces an equivalence of categories.
Prismatic $F$-Gauges and Fontaine--Laffaille modules
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abstract
Let $k$ be a perfect field of characteristic $p$ and $W(k)$ its ring of Witt vectors. We construct an equivalence of categories between the full subcategory of the derived category of quasi-coherent sheaves on the syntomification of $W(k)$ spanned by objects whose Hodge-Tate weights are between $[0,p-2]$ and an appropriate derived category of Fontaine-Laffaille modules.
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math.NT 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
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An integral analogue of Fontaine's crystalline functor
A functor D_crys is constructed that links prismatic F-crystals to filtered Frobenius crystals and, in the Fontaine-Laffaille range, induces an equivalence of categories.