Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compatible systems of $\ell$-adic sheaves   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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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: physics