I have a question about the definition of $\ell$-adic local systems. I understand how to define local systems over any finite extension of $\mathbb{Q}_{\ell}$, but not how to take the "union" of these categories to obtain the category of $\overline{\mathbb{Q}}_{\ell}$-local systems. Any reference or explanation of this construction would be appreciated.
2026-03-27 04:34:23.1774586063
Union of categories and $\ell$-adic local systems
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This construction can be found in Deligne's "La Conjecture de Weil II." Deligne calls it a "2-limite inductive."