2022/04/07 by Shizhang Li, Tong Liu, Li, Shizhang +1
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2204.03411
openalex publication_date 2022/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the maximal finite length submodule of the Breuil-Kisin prismatic cohomology of a smooth proper formal scheme over a p-adic ring of integers. This submodule governs pathology phenomena in integral p-adic cohomology theories. Geometric applications include a control, in low degrees and mild ramifications, of (1) the discrepancy between two naturally associated Albanese varieties in characteristic p, and (2) kernel of the specialization map in p-adic étale cohomology. As an arithmetic application, we study the boundary case of the theory due to Fontaine-Laffaille, Fontaine-Messing, and Kato. Also included is an interesting example, generalized from a construction in Bhatt-Morrow-Scholze's work, which (1) illustrates some of our theoretical results being sharp, and (2) negates a question of Breuil.