# Tagged Questions

**0**

votes

**0**answers

50 views

### Extensions on Higher-dimensional local fields

I have the following question:
Let $M/L$ b a finite extension of n-dimensional local fields and $t_1,\dots, t_n$ a system of local parameters of $L$ with valuation $v$. Let us fix an $1\leq i \leq ...

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**0**answers

36 views

### Valuations in Higher-dimensional local fields

I have the following question which I believ should be true but I would like to have a different opinion about it:
Let $M/L$ is a finite Galois extension of $n$-dimensional local fields and ...

**5**

votes

**0**answers

249 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

**0**answers

598 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 ...

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votes

**3**answers

393 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

**1**answer

552 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

**2**answers

423 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 ...