2024/09/03 by Zeyu Liu, Liu, Zeyu
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2409.02051
openalex publication_date 2024/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X=Spf(OK). We classify perfect complexes of n-truncated prismatic crystals on the prismatic site of X when n≤ 1+(p-1)/(e) by studying perfect complexes on the n-truncated prismatization of X, which are certain nilpotent thickenings of the Hodge-Tate stack of X inside the prismatization of X. We describe the category of continuous semilinear representations and their cohomology for GK with coefficients in BdR,n+ via rationalization of vector bundles on the slight shrinking of the n-truncated prismatization of X. Along the way, we classify certain integral models for de Rham prismatic crystals studied in arXiv:2205.14914.