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Results tagged with galois-theory
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user 6074
Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.
9
votes
Accepted
An explicit isomorphism $K^\times/K^{\times p} \cong K^\flat/\wp K^\flat$ where $K \supset \...
Here is an explicit description of the isomorphism: It takes $a\in K^\flat$ to the class of $1+(\zeta_p-1)^p a^{1/p^n}\in K^\times$ for any large enough $n$ (the image modulo $p$-th powers is independ …
- 21.3k
10
votes
Are absolute Galois groups condensed?
Like any profinite group (or much more general types of topological groups, such as compactly generated ones), you can consider it as a condensed group in the sense of condensed mathematics. In fact, …
- 21.3k
11
votes
1
answer
2k
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Maximal extension almost everywhere unramified and totally split at one place
Fix a finite set of primes $S$ and an additional prime $p$. Let $K$ be the maximal extension of $\mathbb{Q}$ that is unramified outside $S$ and $\infty$ and totally split at $p$. Is the extension $K$ …
- 21.3k