My question is for which varieties over local fields is "independence of l" known for etale cohomology. Say $X/{\mathbb Q}_p$ is a complete non-singular variety and $W_l$ is the (complex) Weil-Deligne representation associated to its etale cohomology group $H^i(\bar X,{\mathbb Q}_l)$. Is it known that $W_l$ is independent of $l\>\>(\ne p)$

a) when $X$ is an abelian variety (with bad reduction)?

b) when $X$ is a variety with potentially good reduction?

c) when $X$ is a variety with potentially semistable reduction?

Any pointers to references or overviews would be very much appreciated!

(Edit: To answer jmc and David Loeffler: by "independence of l" I mean that $W_l$ and $W_{l'}$ have isomorphic Frobenius-semisimplifications. I'd be happy with that!)