Question

Where can I find a complete classification of the $l$-adic Weil-Deligne representations for a local field $F$ of residual characteristic $p$ (with $p$ different from $l$)? Thanks.

Answer 1

Here are the references:

D. Rohrlich. Elliptic curves and the Weil-Deligne group. Elliptic curves and related topics, 125{157, CRM Proc. Lecture Notes, 4, Amer. Math. Soc., Providence, RI, 1994.

or

J. Tate, Number theoretic background.