Questions tagged [class-field-theory]
The class-field-theory tag has no usage guidance.
154 questions with no upvoted or accepted answers
0
votes
0
answers
87
views
Which properties determine the uniqueness of the local Artin map?
Any abelian extension of local fields can be realized as the completion of a global abelian extension. So let $L/K$ be abelian, $w/v$ an extension of places. From the global Artin map on ideles we ...
- 6,180
0
votes
0
answers
133
views
Reciprocity laws in different dimensions
Let $M/L/Qp$ be a finite galois abelian extension of local fields and define
$\mathcal{M}=M\{\{T\}\}=\{\sum_{i\in \mathbb{Z}}a_iT^i:a_i\in M,\min_{i\in \mathbb{Z}}, v(a_i)>−\infty , \lim_{i\to −\...
- 33
0
votes
0
answers
100
views
divisor class group with modulus
Let $C$ be a smooth projective curve over a field $k$ and $S \subset C$ a finite number of points. A modulus is simply a divisor supported on $S$. What is the divisor class group with modulus?
I ...
- 1
0
votes
1
answer
469
views
Finite extensions of residue fields of Henselian DVRs
Let $K$ be an Henselian discrete valuation field such that its completion is separable over $K$. Let $F$ be its infinite residue field. Is it true that a finite extension of $F$ is a simple extension ...
- 2,032