Definition 64.18.8. If $X$ is a separated scheme of finite type over an algebraically closed field $k$ and $\mathcal{F} = \left\{ \mathcal{F}_ n\right\} _{n\geq 1}$ is a $\mathbf{Z}_\ell $-sheaf on $X$, then we define

If $\mathcal{F} = \mathcal{F}'\otimes \mathbf{Q}_\ell $ for a $\mathbf{Z}_\ell $-sheaf $\mathcal{F}'$ then we set

We call these the *$\ell $-adic cohomology* of $X$ with coefficients $\mathcal{F}$.

## Comments (2)

Comment #75 by Keenan Kidwell on

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