stronger Hilbert theorem 90
Let be a field and let be an algebraic closure of
. By we denote the abelian group
and
similarly (here the operation is
multiplication). Also we let
be the absolute
Galois group of .
Theorem 1 (Hilbert 90).
Let be a field.
-
1.
-
2.
-
3.
If , the characteristic
of , does not divide (or ) then
where denotes the set of all -roots of unity
.
References
- 1 J.P. Serre, Galois Cohomology, Springer-Verlag, New York.
-
2
J.P. Serre, Local Fields
, Springer-Verlag, New York.
Title | stronger Hilbert theorem 90 |
---|---|
Canonical name | StrongerHilbertTheorem90 |
Date of creation | 2013-03-22 13:50:27 |
Last modified on | 2013-03-22 13:50:27 |
Owner | alozano (2414) |
Last modified by | alozano (2414) |
Numerical id | 6 |
Author | alozano (2414) |
Entry type | Theorem |
Classification | msc 20J06 |
Synonym | Hilbert 90 |
Related topic | HilbertTheorem90 |