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arXiv · 2402.17755

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

Gleb Terentiuk·Vadim Vologodsky·Yujie Xu
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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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Gleb Terentiuk, Vadim Vologodsky, Yujie Xu. 2024-02-27. Prismatic $F$-Gauges and Fontaine--Laffaille modules. https://doi.org/10.1017/s0010437x26102978

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