Developments since around 1960 have certainly contributed. Before that in his dissertation used Hilbert modular forms to study abelian extensions of real quadratic fields. Complex multiplication of abelian varieties was an area opened up by the work of Shimura and Taniyama. This gives rise to abelian extensions of CM-fields in general. The question of which extensions can be found is that of the Tate modules of such varieties, as Galois representations. Since this is the most accessible case of ℓ-adic cohomology, these representations have been studied in depth.
