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

Gleb Terentiuk; Vadim Vologodsky; Yujie Xu

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

Number Theory 2025-07-08 v2 Algebraic Geometry

Authors: Gleb Terentiuk , Vadim Vologodsky , Yujie Xu

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.

Keywords

prismatic F-gauges Fontaine-Laffaille modules syntomification Hodge-Tate weights Witt vectors derived category

Cite

@article{arxiv.2402.17755,
  title  = {Prismatic $F$-Gauges and Fontaine--Laffaille modules},
  author = {Gleb Terentiuk and Vadim Vologodsky and Yujie Xu},
  journal= {arXiv preprint arXiv:2402.17755},
  year   = {2025}
}

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v2; 50 pages

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

Abstract

Keywords

Cite

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