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arXiv · 2101.00846

Compatible systems of $\ell$-adic sheaves

Quentin Guignard
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Abstract

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

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Quentin Guignard. 2021-01-04. Compatible systems of $\ell$-adic sheaves. https://arxiv.org/abs/2101.00846

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