2025/10/15 by Keiho Matsumoto, Matsumoto, Keiho
Engineering · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2510.13596
openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
We construct a covariant realization functor, denoted Solidm, from the category of motives with modulus to the derived category of solid modules in the sense of Clausen--Scholze. For any smooth modulus pair (X, D), the dual of Solidm(X, D) recovers the Hodge realization of Kelly--Miyazaki for (X, D). Using Ren's pro-solid comparison theorem, we give an explicit description of Solidm(X, D) and compute Solidm of the cone of M(U, D restricted to U) → M(X, D), in the setting where X is a smooth proper variety over a field, D ⊂ X is a simple normal crossings divisor, and U ⊂ X is an open immersion. We identify the result via the formal completion of X along the complement X ∖ U.