All Questions
Tagged with valuation-theory local-fields
4 questions
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
12
votes
1
answer
778
views
Is every Polish ring topology on $\mathbb{C}$ defined by an absolute value?
There is a unique up to isomorphism algebraically closed field of characteristic 0 and cardinality of the continuum. Let's call it $K$.
We usually call it $\mathbb{C}$, but by this we impose a ...
- 11.6k
3
votes
0
answers
437
views
Relation between ramification index and length of filtration of ramification groups
Given a complete valued field $K$ with a discrete value group $\mathbb{Z}$, consider a totally ramified finite Galois extension $L$ of $K$ with its Galois group $G$. Let $O_L$ be the valuation integer ...
- 131
6
votes
3
answers
1k
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Finite extension of local fields
Can a (higher) local field have uncountably many finite (seperable) extensions?
- 11.3k