2025/05/06 by Maximilian Hauck, Hauck, Maximilian
Engineering · Environmental Science · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Groundwater flow and contamination studies #Hydraulic flow and structures #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2505.03546
openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
We use the approach to p-adic cohomology theories via stacks recently developed by Drinfeld and Bhatt--Lurie to formulate a stacky version of a comparison result between the Nygaard filtration on prismatic cohomology and the Hodge filtration on de Rham cohomology by Bhatt--Lurie and thereby also obtain a generalisation in the case of smooth and proper p-adic formal schemes which allows for coefficients in an arbitrary gauge. In the process, we develop a stacky approach to diffracted Hodge cohomology as introduced by Bhatt--Lurie which also captures the conjugate filtration and the Sen operator. In the appendix, we also introduce a stack computing the conjugate filtration on absolute Hodge--Tate cohomology.