2024/01/04 by Kimihiko Li, Li, Kimihiko
Mathematics · #14F20 #14F30 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2401.02057
openalex publication_date 2024/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we construct two kinds of de Rham-like complexes which compute the cohomology of complete crystals on the higher-level q-crystalline site, which was introduced in a previous article of the author. One complex is the q-analog of the higher de Rham complex constructed by Miyatani, and another complex is the q-analog of the jet complex constructed by Le Stum-Quirós. The complexes we construct can also be regarded as the higher-level analogs of the q-de Rham complex.