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Results tagged with global-fields
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user 4149
6
votes
Accepted
The second Tate-Shafarevich group of a permutation module is trivial
We write $G_w={\rm Gal}(L_w/K_v)$.
Definition. For $n\ge 1$, we denote
$$Ш_\omega^n(G,M)=\ker\Big(H^n(G,M)\to\prod_C H^n(C,M)\Big)$$
where $C$ runs over the cyclic subgroups of $G$.
Remark. $Ш^2(L …
- 14.2k
2
votes
0
answers
62
views
Constructing a cyclic extension $L$ with given local behavior of a global field $K$ such tha...
Let $F$ be a global field without real places
(that is, a function field or a totally imaginary number field).
Let $K/F$ be a cyclic extension of degree $n$.
Let $S$ be a ${\rm Gal}(K/F)$-invariant fi …
- 14.2k