All Questions
9 questions with no upvoted or accepted answers
12
votes
0
answers
272
views
sequences in non-abelian group cohomology
In general, if we have a (pro-)finite group $G$ and a sequence of (continuous) non-abelian $G$-modules $$1\rightarrow A\rightarrow B\rightarrow C\rightarrow 0,$$ such that the image of $A$ lies in the ...
- 273
10
votes
0
answers
600
views
A formal group scheme in explicit local class field theory
Let $K$ be a nonarchimedean local field with residue field $k$ of characteristic $q = p^N$, and pick a uniformizer $\pi\in \mathscr{O}_K$. Recall that explicit local class field theory, à la Lubin--...
- 5,770
6
votes
0
answers
513
views
Extensions of p-adic number fields
Let $p$ be a prime number and $\mathbb{Q}_p$ be the $p-$adic rational field. Let $E/\mathbb{Q}_p$ be a fixed finite extension. On this site, I define a finite extension $F/E$ to be "good" if ...
- 71
5
votes
0
answers
758
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 Q_p,...
- 51
4
votes
0
answers
190
views
Is $K^{ur} K^{\pi} = L$?
Let $L/K$ be a finite extension of $p$-adic fields, $\pi$ a uniformizer of $K$, $\theta = (-, L/K)$ the local Artin map $K^{\ast} \rightarrow Gal(L/K)$, $E$ be maximal unramified extension of $K$ ...
- 6,180
2
votes
1
answer
252
views
Ring structure on Brauer group
Class field theory defines an isomorphism between the Brauer group of a finite extension of p-adic fields and a cyclic group with a canonical generator. This in turn defines an isomorphism of the ...
- 447
2
votes
0
answers
116
views
Restriction of the local Artin map on the valuation ring of a local field
Let $F$ be a local field, in particular a finite extension of $\mathbb{Q}_p$ for some prime $p$ and let $Art_{L}: L^\times \to Gal(F^{ab}/F)$ be its local Artin map. We know that if $L/F$ is a finite ...
- 367
2
votes
0
answers
128
views
Lubin--Tate formal group construction in local class field theory using group cohomology
Let $K$ be a non-archimedean local field of characteristic 0. Fix a uniformiser $\pi$ and an algebraic closure $\bar{K}$. The theory of Lubin--Tate formal groups gives an explicit construction of the ...
- 1,428
2
votes
0
answers
433
views
Global Artin reciprocity law from Local class field theory
Let $K=\mathbb F_q((t)), p -$ prime ideal in $K$, $\psi_p$ be the local Artin map$K_p^* \to Gal(K_p^{ab}/K_p)=G_p \subset Gal(K^{ab}/K)$. Then I define global Artin map $\psi_K$as product of $\psi_p$, ...
- 71