That is to say, χ = { χℓ }ℓ is a "family" of ℓ-adic representations χ ℓ : G Q → GL 1 ⁡ ( Z ℓ ) {\displaystyle \chi _{\ell }:G_{\mathbf {Q} }\rightarrow \operatorname {GL} _{1}(\mathbf {Z} _{\ell })} satisfying certain compatibilities between different primes.
I andra ord är χ = { χℓ }ℓ en "familj" av ℓ-adiska representationer χ ℓ : G Q → GL 1 ⁡ ( Z ℓ ) {\displaystyle \chi _{\ell }:G_{\mathbf {Q} }\rightarrow \operatorname {GL} _{1}(\mathbf {Z} _{\ell })} som satisfierar flera kompatibilitetskrav mellan olika primtal.