Divided prismatic Frobenius crystals of small height and the category MF

2023/05/10 by Würthen, Matti
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2305.06081

Abstract

Let X be a smooth p-adic formal scheme over a mixed characteristic complete discrete valuation ring O_K with perfect residue field. We introduce a general category MF_{[0, p-2]}^tor-free(X) of p-torsion free crystalline coefficient objects and show that this category is equivalent to the category of completed prismatic Frobenius crystals of height p-2, recently introduced by Du-Liu-Moon-Shimizu. In particular this shows that the category MF^tor-free_{[0, p-2]}(X) is equivalent to the category of crystalline ℤ_p-local systems on X with Hodge-Tate weights in \0,… , p-2\, which generalizes the crystalline part of a theorem of Breuil-Liu to higher dimensions.

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