Jump sets in local fields

Abstract: I will explain how three themes of the theory of local fields can be simultaneously
understood by means of simple combinatorial objects which I call jump sets. Namely jump
sets will provide the following:
1) A parametrization of the structures of principal units as filtered modules.
2) A parametrization of Galois sets as metric spaces.
3) A parametrization of all the possible jumps of cyclic extensions of a local field.
Jump sets comes naturally with a "combinatorial" measure (which one can compute): it turns
out that when one counts the number of local fields (weighted with Serre mass formula) having
a given jump set one gets exactly the combinatorial measure of the jump set.
Often the jump set may be recognized by an Eisenstein polynomial: so one is provided
with very explicit invariants of Eisenstein polynomials coming from the structure of the
principal units as a filtered module and from ramification theory at the same time. This
offers a precise link between 1) and 2).
In the end I will hint at further results on this topic, and at some further questions.