Compatible systems of $\ell$-adic sheaves

Abstract

We introduce a notion of compatibility for families $({\mathcal{F}}_{\ell }{)}_{\ell }$ of bounded constructible $\ell$-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 $\epsilon$-factors introduced recently by the author. We establish independence of $\ell$ for the characteristic cycles and characteristic $\epsilon$-cycles of compatible families.

23 p