Let $X$ be a smooth algebraic variety of dimension $n$ over a field $k$. Let $\Omega_X$ be the sheaf of differentials (over $k$). Then we may consider the deRham complex $$\Omega_X^\bullet= \mathcal{O}_X\to \Omega_X\to \wedge^2\Omega_X\to \cdots $$
The deRham cohomology is then the hypercohomology of $\Omega_X^\bullet$.
What I am confused about is how exactly one is allowed to take this hypercohomology. Sheaf cohomology on schemes is computed for $\mathcal{O}_X$ modules, but the arrows in the complex $\Omega_X^\bullet$ are not $\mathcal{O}_X$ linear (only $k$ linear). How do you take the hypercohomology then?
Thanks for any help or direction.