Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.16683 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918144893779968 |
|---|---|
| author | Cao, Kaixing |
| author_facet | Cao, Kaixing |
| contents | In this paper, we construct a monoidal weight structure on the stable $\infty$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16683 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Weight Structure on Rigid Analytic Motives over a Field Cao, Kaixing Algebraic Geometry Number Theory In this paper, we construct a monoidal weight structure on the stable $\infty$-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. |
| title | A Weight Structure on Rigid Analytic Motives over a Field |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2509.16683 |