Slopes and weights of ℓ-adic cohomology of rigid spaces

2025/02/08 by Qing Lu, Weizhe Zheng, Lu, Qing +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #advanced mathematical theories

paper · pdf · doi:10.1016/j.aim.2026.111149

Abstract

We prove that Frobenius eigenvalues of ℓ-adic cohomology and ℓ-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.

Citations

• The six functors for Zariski-constructible sheaves in rigid geometry
• Compatible systems and ramification
• Altered local uniformization of Berkovich spaces
• A comparison theorem for l-adic cohomology
• Mixed perverse sheaves for schemes over number fields
• Good Reduction of Abelian Varieties

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