Definition 12.5
(Inverse different)
.
The
inverse different
is
D
L
∕
K
−
1
=
{
y
∈
L
:
Tr
L
∕
K
(
x
y
)
∈
O
K
∀
x
∈
O
L
}
,
an
O
L
submodule of
L
.