2024/05/20 by Nakkajima, Yukiyoshi
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2405.12045
For a flat p-adic formal family S of log points over a complete discrete valuation ring with perfect residue field of mixed characteristics (0,p) and for a simple normal crossing log scheme X over an exact closed log subscheme of S defined by an element of the maximal ideal of the dvr, we construct two fundamental filtered complexes in the convergent topos the underlying scheme of X over the underlying scheme of S. We prove that they are canonically isomorphisc. Because one of the complex is shown to calculate the log convergent cohomology sheaf of X/S, the filtered complex produces the weight filtration on the log convergent cohomology sheaf if the underlying scheme of X is proper over the underlying scheme of S. We give a comparison theorem between the projection of the filtered complex in the Zariski topos of the underlying scheme of X and the isozariskian weight-filtered complex constructed in the author's previous work.