2022/01/25 by Gao, Hui · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2201.10136
Let K be a mixed characteristic complete discrete valuation field with perfect residue field, and let K_∞/K be a Kummer tower extension by adjoining a compatible system of p-power roots of a chosen uniformizer. We use this Kummer tower to reconstruct Sen theory which classically is obtained using the cyclotomic tower. Using this Sen theory over the Kummer tower, we prove a conjecture of Min-Wang which predicts that Hodge-Tate prismatic crystals are determined by the Sen operator; this implies that the category of (rational) Hodge-Tate prismatic crystals is equivalent to the category of nearly Hodge-Tate representations.