Let $X$ be a smooth projective algebraic variety over a field of characteristic zero and let $D$ be a simple normal crossing divisor on $D$. Put

$j: U \hookrightarrow X$

for the inclusion of the complement $U=X-D$ on $X$.

Are the functors $j_\ast$ and $j_!$ exact?

I think the answer is yes.

I would be very grateful if someone could provide me with a proof.