?? maybe i'll take a stab at trying to re-invent langlands reciprocity (??? ...) here ....

?? so... ?? maybe we're supposed to start with a "galois representation" of some sort (?? probably really a functor of some kind ....) ... ??? and then get from this an "automorphic representation", whatever that is .... ??? ...

??? but let's try fleshing it out a bit ... ???....

?? "galois representation" meaning something like representation of "absolute galois group" of certain "base field" k .... ??? really some sort of functor from some sort of commutative k-algebras to some sort of vector spaces .... ????say over some field
(???) k' ... ???? .....

??now what does "automorphic representation" mean here ???? .....

?? well, first let me try picking some plausible guesses as to what k and k' and so forth might be in some simple but maybe not too simple example ....

k = imaginary quadratic field ....

k' = p-adics ?? ....

galois representation = ... ???? torsion points ... ???.... on corresponding (...) elliptic curve ... ?? ....

???? and then .... "automorphic representation" being representation (?????) of _something_ "over k" ???? ..... ????

??any idea how to get "l-function" of galois rep and/or of automorphic rep here ??? ....


??? "adeles" .... ????? of k ????? .... ????



???trying to get "abelian variety with generalized complex multiplication" (??? ...) from ... "number-flavored dimensional theory" .... ????? .....


?? try making table of galois reps ....

p-torsion of gl(1) ... ???? ??? gl(1)'s involved here ??? ...

p-torsion of elliptic curve with complex multilication ... ???....

????? ....