The lower ramification groups of a finite Galois extension 
of local fields, with Galois
group 
and normalized discrete valuation 
, are
 |
Here 
and 
is the valuation on 
. The zeroth ramification group 
is the inertia subgroup,
and 
is the wild inertia subgroup.
The upper ramification groups 
are obtained by reindexing the lower ramification groups
using the Herbrand function. Unlike lower numbering, upper numbering is preserved
when the Galois group is replaced by a quotient.
