Publication details
The relative Hodge–Tate spectral sequence for rigid analytic spaces
Abstract
We construct a relative Hodge–Tate spectral sequence for any smooth proper morphism of rigid analytic spaces over a perfectoid field extension of (Formula presented.). To this end, we generalise Scholze's strategy in the absolute case by using smoothoid adic spaces. As our main additional ingredient, we prove a perfectoid version of Grothendieck's “cohomology and base-change”. We also use this to prove local constancy of Hodge numbers in the rigid analytic setting, and deduce that the relative Hodge–Tate spectral sequence degenerates.
Details
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Article
- Journal
- Journal of the London Mathematical Society
- Volume
- 112
- ISSN
- 0024-6107
- Publication date
- 15.10.2025
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- General Mathematics
- Electronic version(s)
-
https://doi.org/10.1112/jlms.70318 (Access:
Open
)
