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Mathematics, Algebraic Geometry, Number Theory
Abstract:
We introduce a notion of compatibility for families (Fℓ)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.
