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Prismatic $F$-Gauges and Fontaine--Laffaille modules

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arxiv 2402.17755 v2 pith:Q5MYQBLG submitted 2024-02-27 math.NT math.AG

Gleb Terentiuk , Vadim Vologodsky , Yujie Xu This is my paper · ORCID
classification math.NTmath.AG
keywords categoryderivedmodulesappropriatecategoriescharacteristicconstructequivalence
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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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  1. An integral analogue of Fontaine's crystalline functor

    math.NT 2025-04 conditional novelty 7.0 of 10

    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.

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