2025/09/20 by Cao, Kaixing
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2509.16683
In this paper, we construct a monoidal weight structure on the stable ∞-category of rigid analytic motives over a local field K via Galois descent. This extends the weight structure on the full subcategory of rigid analytic motives with good reduction, which is defined by Binda-Gallauer-Vezzani. As an application, we show that the Hyodo-Kato realization factors through the weight complex functor studied by Bondarko and Sosnilo. In particular, the weight complex yields a spectral sequence converging to the Hyodo-Kato cohomology of smooth quasi-compact K-rigid analytic spaces, thereby inducing a weight filtration on it.