 In fact, formula_3 is a continuous homomorphism (where the topology on "G" is the Krull topology, and that on Z"p"× is the p-adic topology).By varying ℓ over all prime numbers, a compatible system of ℓ-adic representations is obtained from the ℓ-adic cyclotomic characters (when considering compatible systems of representations, the standard terminology is to use the symbol ℓ to denote a prime instead of "p").That is to say, χ = { χℓ }ℓ is a "family" of ℓ-adic representations

satisfying certain compatibilities between different primes.