It led to many results within the Zimmer Program, although many of the main conjectures remain open.

There are two main conjectures known as the Hadwiger conjecture or Hadwiger's conjecture:

Other generalizations of the main conjecture proved using the Euler system method have been found by Karl Rubin, amongst others.

In each case, there is a main conjecture linking the tower to a p-adic L-function.

Mazur and Wiles had earlier worked together on the main conjecture of Iwasawa theory.

Ragsdale's main conjecture is as follows.

It was proved by as a corollary of their work on the main conjecture of Iwasawa theory.

It is now known in many cases, and would follow in general from the main conjectures of minimal model theory, notably the abundance conjecture.

The Herbrand-Ribet theorem and the Gras conjecture are both easy consequences of the main conjecture.

There are several generalizations of the main conjecture, to totally real fields, CM fields, elliptic curves, and so on.