?? functor from abelian closures of imaginary quadratic number field k to [z/p]-vector spaces .... assigning to closure c the vector space of ("strict" ...) p-torsion points on elliptic curve x (with complex multiplication wrt k ...) ...

??? maybe getting from this a representation of gl(2,j-adeles(k)) ... where j is ... amount of ramification needed for getting the p-torsion points .... ????? ..... ?????? .......

??? integer ring of k as acting by endomorphisms on x .... ??so maybe acting by endomorphisms on strict p-torsion of x ??? .....

???maybe .... this as some really obvious module of int(k) .... ????? ??? and this statement as more or less just jugendtraum here .... ????? .... ????.......

??? trying to identify p-torsion points on elliptic curve with complex multiplication as being almost just like corresponding imaginary quadratic number ring ... ???? ..... ???? maybe with the identification map being ambiguous up to something ???? ...... ????? .....

????? cyclotomic case ????? .......

???? elliptic curve with complex multiplication as some sort of direct limit of stuff whose inverse limit is profinite completion of corresponding int(k) ... ?????? ....... ???????? ....... ???????? .......

???? fourier duality between elliptic curve and corresponding imaginary quadratic number ring .... ???? ..... ... complex numbers .... ??? archimedean vs non-archimedean ... ???????? ........ ?????? ......

?? ... values of elliptic function at elements of corresponding imaginary quadratic number ring .... ???? ...... or of fractional ideal therein ???? ..... ?????? .......

??? level slip here ???????? ..... ????? ......

????? frobenius .... ????? ......

????? combined action of int(k) and absolute abelian galois group of k on strict p-torsion points of corresponding x .... ????? ..... ??????? ......

2-step solvable galois group here ... ?????? .....

????hmmmm ....... i wrote:

"??? trying to identify p-torsion points on elliptic curve with complex multiplication as being almost just like corresponding imaginary quadratic number ring ... ???? ..... ???? maybe with the identification map being ambiguous up to something ???? ...... ????? ....."

... ??? maybe the something that it's ambiguous up to is ess just the (second ... ?? ...) galois group here ????? ...... ??? .....

??? quotient ring (?field?) of int(k) as rep of certain partial galois group ... ???? ...... ??? l-function of such rep ??? .... ????? ....

quotient ring int(k)/j as representation of j-absolute abelian galois group of k ???? ..... ????? ..... ??????? .....