Let $k$ be an algebraically closed field, and $X$ be a smooth variety. For any compactification $i: X \hookrightarrow Y$ (so $X$ is a dense open subset of $Y$), consider the induced map $i_!: H^i_{et,c}(X, \mathbb Z_l) \rightarrow H^i_{et,c}(Y,\mathbb Z_l)$ between compact supported etale cohomology groups.

Is $Ker(i_!)$ independent of the compactification (at least for $\mathbb Q_l$ coefficients )?