New answers tagged local-fields
0
votes
Reference request: Discriminant of a $V_4$-extension of local fields is the product of discriminants of intermediate fields
The following remarks concern the case where the base field is $\mathbb Q$.
It is of course perfectly possible to compute the discriminant by writing down integral bases; this is not too difficult and ...
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.
- 12.8k
2
votes
Accepted
Unramified composition for every extension
The Abhyankar construction can be generalized naturally as follows: For each $p\in S$, take the (finite) set of Galois extensions $F_p/K_p$ occurring as completions of the Galois closure of a degree-$...
- 2,513
Top 50 recent answers are included