2020/12/23 by Yukiyoshi Nakkajima, Nakkajima, Yukiyoshi
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2012.12981
openalex publication_date 2020/12/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We construct a theory of the derived PD-Hirsch extension of the log crystalline complex of a log smooth scheme and we construct a fundamental filtered dga (H_\rm zar,\rm TW,P) and a fundamental filtered complex (H\rm zar,P) for a simple normal crossing log scheme X over a family of log points by using the log crystalline method in order to overcome obstacles arising from the incompatibility of the p-adic Steenbrink complexes in [M] and [Nak4] with the cup product of the log crystalline complex of X. When the base log scheme is the log point of a perfect field of characteristic p>0, we prove that (H_\rm zar,\rm TW,P) and (H\rm zar,P) is canonically isomorphic to Kim and Hain's filtered dga and their filtered complex in [KH], respectively.