Theorem 13.3.
Assuming that:
L
∕
K
a finite separable extension of
non-archimedean
local fields
Then
there exists a field
K
0
,
K
⊆
K
0
⊆
L
and such that
(i)
K
0
is
unramified
(ii)
L
∕
K
0
is
totally ramified
Moreover
[
L
:
K
0
]
=
e
L
∕
K
,
[
K
0
:
K
]
=
f
L
∕
K
and
K
0
∕
K
is Galois.