5
votes
0answers
241 views

maximal abelian extension of quadratic extension of $\mathbb Q_p$

I read this article "Local class field theory via Lubin-Tate theory" http://arxiv.org/pdf/math/0606108v2.pdf. And I want to find the maximal abelian extensions for quadratic extensions of $\mathbb ...
6
votes
0answers
567 views

Automorphisms of local fields

It is an amusing coincidence (at least it appears to be a coincidence to me) that any completion of the field $\mathbb{Q}$ has trivial automorphism group as an abstract field, i.e. when ignoring the ...
0
votes
3answers
387 views

Brauer group of complete DVR

Let $A$ be a complete discrete valuation ring with fraction field $K$ and perfect residue field $\kappa$. Let $K_{nr}$ be the maximal unramified extension of $K$ and let $A_{nr}$ be its ring of ...
2
votes
1answer
544 views

Q_p*/(Q_p*)^2 and descent for elliptic curves

Is there a simple description of the group Q_p*/(Q_p*)^2 where Q_p denotes the p-adic integers? I am doing descent calculations for elliptic curves, and so am most interested in the case p = 2. ...
3
votes
2answers
414 views

What are the open normal subgroups of the inertia group of a local field?

Let $K$ be a non-Archimedean local field, i.e., complete with respect to a non-trivial, non-archimedean discrete absolute value, with finite residue field $k$ of characteristic $p\neq 0$. Also let ...