?? so at the moment (after discussion with todd this morning ...) the idea seems to be something like ... ?? for a nice (?? in sense described by shimura, maybe??) abelian-variety-with-complex-multiplication, the galois representation (??wrt the absolute galois group of the associated number field, that is ... ??? ... ?? rather than of the absolute galois group of Q, for example ...) that you get from p-torsion points of the variety breaks up into 1d representations of that galois gp ... meaning that it's really just a rep of the abelianized galois group ... ???? and kronecker's jugendtraum (???as generalized to some extent by taniyama and shimura, for example ?? ... ?? and intermingled with artin reciprocity ... ?? ...) can be interpreted as giving some sort of nice explicit description of those 1d reps .... ????? ....

(meanwhile todd and i are struggling to get even the most basic calculations along these lines to work out .... lemniscate inflection points ... ?? ....)

??? and then maybe the langlands program will have a lot to do with what happens in the case of an abelian-variety-without-complex-multiplication ... presumably now the 2d rep is typically irreducible .... ????? ....

??? and maybe the modularity theorem as specialized to the complex-multiplication case will have to do with relationship between "elliptic" (?? ... evaluating elliptic functions at torsion points ...) and "modular" (?? ... evaluating modular functions at ideals in imaginary quadratic number fields .... "turning ideal numbers into actual numbers" ....) versions of jugendtraum .... ??? .... ??????? ...... ?? but then will somehow also be very interesting in without-complex-multiplication case .... ???? .....

?? seems promising to try to understand stuff about ... ??? hecke operators acting on modular forms .... and so forth ...

??but also ... ??? i want to try again with my semi-ancient homegrown attempt to "directly use hecke operators associated to geometry of finite galois group to construct higher-dim galois rep" .... ???? ..... ??? 3! as galois group ??? ..... ???hmm, but does langlands program / conjectures make _any_ sort of claim about _this_ kind of galois rep ??? ....

???possibility of relationship to issue of "galois rep" as misconceived version of some sort of functor defined not only on algebraically closed fields but on some more general class of fields and / or rings ... ??? .... (?? see further discussion in later posts ... ???? .....)