Compatible systems of ℓ-adic sheaves

2021/01/04 by Quentin Guignard, Guignard, Quentin
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14F20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2101.00846

openalex publication_date 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of compatibility for families (F_ℓ)_ℓ of bounded constructible ℓ-adic complexes of étale sheaves on schemes. For schemes of finite type over a field, this notion is preserved by the usual six functors. We prove that the compatibility of a family is preserved by the nearby cycles functor and by the linearized ε-factors introduced recently by the author. We establish independence of ℓ for the characteristic cycles and characteristic ε-cycles of compatible families.

Citations

• Constructible sheaves are holonomic
• Geometric local epsilon factors

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• The pro-étale topology for schemes
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