On Euler systems for the multiplicative group over general number fields

The equivariant Tamagawa number conjecture for abelian extensions of imaginary quadratic fields

“…Each complex D n is then a complex of finitely generated Z p -modules, hence of compact Hausdorff spaces. The inverse limit functor therefore commutes with taking cohomology and so claim (b), and the second part of claim (a), follow by taking the limit of the respective statements for the complexes D n as given in [12,Prop. 3.1 (i)].…”