??? these galois representations we seem to be imagining at the moment .... ??expressed as functors ........ ??????...... from algebraic closures of given number field k, to ... ??? modules of .... ??? .... ?????

k number field ....

j ideal in k .... ?? ....

?? assign to each algebraic closure x of k the int(k)/j-module given by homming int(x) into int(k)/j .... ???? over .... ????? or.... as .... ???? module of something ????.....