What question did this study set out to answer?

The research aims to establish a categorical equivalence involving quasi-coherent sheaves and Fontaine–Laffaille modules.

June 18, 2026Open Access

Prismatic F -gauges and Fontaine–Laffaille modules

Key Points

The research aims to establish a categorical equivalence involving quasi-coherent sheaves and Fontaine–Laffaille modules.
Constructed a full subcategory of derived categories on syntomification of W(k).
Focused on objects with Hodge–Tate weights between [0, p-2].
Demonstrated a precise equivalence between the specified categories.
Outlined the implications for the structure of Fontaine–Laffaille modules.

Abstract

ABSTRACT Let k be a perfect field of characteristic p and let W (k) be 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 left bracket 0 comma p minus 2 right bracket 0, p − 2 0, p-2 and an appropriate derived category of Fontaine–Laffaille modules.

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