we will discuss our recent proof (joint work with c. greither) of a conjecture linking $\ell$--adic realizations of $1$-motives and special values of equivariant $l$--functions in characteristic $p$, refining earlier results of deligne and tate. as a consequence, we give proofs (in the characteristic $p$ setting) of various central classical conjectures on special values of $l$--functions, namely those due to coates-sinnott, brumer-stark, and gross. if time permits, we will indicate how this theory can be extended to characteristic $0$.