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Galois cohomology
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Galois cohomology
In
mathematics
,
Galois cohomology
is the study of the
group cohomology
of
Galois modules
, that is, the application of
homological algebra
to
modules
for
Galois groups
. A Galois group
G
associated to a
field extension
L
/
K
acts in a natural way on some
abelian groups
, for example those constructed directly from
L
, but also through other
Galois representations
that may be derived by more abstract means. Galois cohomology accounts for the way in which taking Galois-invariant elements fails to be an
exact functor
.
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