All Questions
Tagged with valuation-theory reference-request
8 questions
26
votes
3
answers
6k
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An unfamiliar (to me) form of Hensel's Lemma
In his very nice article
Peter Roquette,
History of valuation theory. I. (English summary) Valuation theory and its applications, Vol. I (Saskatoon, SK, 1999), 291--355,
Fields Inst. Commun., ...
- 65.4k
8
votes
2
answers
496
views
Literature on non-Archimedean analogues of basic complex analysis results
It looks like there is some literature out there on what might be called 'non-Archimedean complex analysis' e.g. Benedetto - An Ahlfors Islands Theorem for non-archimedean meromorphic functions and ...
4
votes
0
answers
335
views
Reference for “approximately henselian” valued fields
I need some valuation theory in a paper I’m working on. This is not quite within my area of expertise, and I’d like to make the terminology right.
A valued field $(K,v)$ with value group $\Gamma$, ...
- 47.7k
3
votes
0
answers
96
views
Luroth's theorem for Discrete valuation rings?
Luroth's theorem states that if $k$ is a field and $L$ is a field extension of $k$ such that $k \subset L \subseteq k(X)$, then $L=k(f(X))$ for some $f(X) \in k(X) $ . My question is ; is there any ...
user111524
3
votes
0
answers
274
views
Is the special case of Abhyankar's lemma is also considered as such?
Consider the following statement:
Assume $E$ and $F$ are unramified (over some fixed prime) finite separable extensions of a field $K$. Then $EF$ is also unramified.
I always thought that it is ...
- 3,362
2
votes
0
answers
107
views
Request for bibliographic information
Greetings to everyone on this forum (I am a new-comer). I would like to ask the experienced members for suggestions on (as) comprehensive and systematic (as possible) bibliographic sources regarding:
...
- 121
1
vote
1
answer
142
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Valuation theory on semisimple algebras used in the paper of Cohen-Martinet: reference request
I'm currently reading the paper of Henri Cohen & Jacques Martinet "Etude heuristique des groupes de classes des corps de nombres"
On the 2nd section, they recall some facts on valuations, ...
- 1,013
1
vote
0
answers
187
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How to prove that $k(x)$ is not complete in the $x$-adic metric [closed]
It is not hard to find proofs showing that $\mathbb{Q}$ is not complete with respect to the metric induced by the valuation $|\;\;|_p$.
For example, it is enough to recall that every complete metric ...
- 596