I'm studyng a course on class field theory and Galois cohomology this semester, and my lecturer said in one of the lectures that the Tata-Shafarevich group is indeed important is class field theory, and he mentioned that this group has a role in computing the Brauer group of some field, bet he didn't mentioned more than that.
What are the applications of the Tate-Shafarevich gruop in class field theory? I know we can prove some properties of this group by the Selmer group which is close to class field theory, but I'm intrested in the applications of the other direction.
Thanks in advance.