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Revision difference : Hilbert Theorem 90 |
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Version 1 |
| Let $L/K$ be a finite Galois extension with Galois group $G = \operatorname{Gal}(L/K)$. Then the first Galois cohomology group $H^1(G, L^*)$ is 0. |
Let $L/K$ be a finite Galois extension with Galois group $G = \operatorname{Gal}(L/K)$. Then the first Galois cohomology group $H^1(G, L^*)$ is 0. |
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| A corollary (and the actual result that Hilbert called his Theorem 90) is that, if $G$ is cyclic with generator $\sigma$, then $x \in L$ has norm 1 if and only if |
A corollary (and the actual result that Hilbert called his Theorem 90) is that, if $G$ is cyclic with generator $\sigma$, then $x \in L$ has norm 1 if and only if |
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| x = y/\sigma(y) |
x = y/\sigma(y) |
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| for some $y \in L$. |
for some $y \in L$. |
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