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Results tagged with local-fields
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user 35416
9
votes
Accepted
A remark of Mordell alluding to a local/global principle for cubic Diophantine equations
As Franz says, Mordell is talking about the conjecture of Birch and Swinnerton-Dyer. But I just wanted to add that in the modern formulation of the conjecture, it is not easy to discern the original h …
- 13k
3
votes
Accepted
Existence of tamely ramified tower of extension over $\mathbb{Q}_p$
No, such a field does not exist, since the Galois group of $k_{tr}/k_{nr}$ embeds into the multiplicative group of the residue field of $k_{nr}$, which your hypothesis implies to be finite.
- 13k
2
votes
Brauer group of complete DVR
The proof of this is spelled out very clearly and nicely by Serre in Cassels and Fröhlich, Algebraic Number Theory. He does it for the fields, rather than their rings of integers, i.e. $\text{Br}(K)\c …
- 13k