## 59.7 Nontorsion coefficients

To study nontorsion coefficients, one makes the following definition:

$H_{\acute{e}tale}^ i (X, \mathbf{Q}_\ell ) := \left( \mathop{\mathrm{lim}}\nolimits _ n H_{\acute{e}tale}^ i(X, \mathbf{Z}/\ell ^ n\mathbf{Z}) \right) \otimes _{\mathbf{Z}_\ell } \mathbf{Q}_\ell .$

The symbol $\mathop{\mathrm{lim}}\nolimits _ n$ denote the limit of the system of cohomology groups $H_{\acute{e}tale}^ i(X, \mathbf{Z}/\ell ^ n\mathbf{Z})$ indexed by $n$, see Categories, Section 4.21. Thus we will need to study systems of sheaves satisfying some compatibility conditions.

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