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.