Publikationsdetails
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
- Organisationseinheit(en)
-
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
- Typ
- Artikel
- Journal
- Journal of the London Mathematical Society
- Band
- 112
- ISSN
- 0024-6107
- Publikationsdatum
- 15.10.2025
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Allgemeine Mathematik
- Elektronische Version(en)
-
https://doi.org/10.1112/jlms.70318 (Zugang:
Offen
)
