Slopes and weights of ℓ-adic cohomology of rigid spaces
Abstract
We prove that Frobenius eigenvalues of $\ell$-adic cohomology and $\ell$-adic intersection cohomology of rigid spaces over $p$-adic local fields are algebraic integers and we give bounds for their $p$-adic valuations. As an application, we deduce bounds for their weights, proving conjectures of Bhatt, Hansen, and Zavyalov. We also give examples of monodromy-pure perverse sheaves on projective curves with non monodromy-pure cohomology, answering a question of Hansen and Zavyalov.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
advanced mathematical theories
Publication details
- Journal / source
- Advances in Mathematics
- Volume
- 502
- Pages
- 111149–111149
- Publication date
- 21 July 2026
- Language
- EN