x imaginary quadratic number ring ... ?? (x # c) / x .... "additive" complex lie gp .... ??? algebraic ?? ... ?? in somewhat unambiguous way ?? ... iso to (c,+) + "elliptic curve with complex multiplication" ??? .... ??? ....

?? confusion here ?? .... ??? non-dependence on multiplication .... ???? .... ?? ....

x -> c^2 .... a+bj |-> (a+bj, a-bj) .... ???? .... ?? (2a,2bj) ??? .... maybe just silly mistake before ??? .... ????? ...

?? subcyclotomic but not cyclotomic field .... ?? fourier duality ... ?? .... ???? .....

??? tensor product of abelian varieties .... hom of them .... ??? shimura & taniyama book .... ??? ....