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Results tagged with galois-theory
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user 82229
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.
2
votes
0
answers
134
views
complex numbers over algebraic numbers, continuous cohomology
This question is related to this one. Choose an embedding $\overline{\mathbf{Q}}\rightarrow \mathbf{C}$ from the algebraic closure of the field of rational numbers to the field of complex numbers. Is …
- 1,613
7
votes
1
answer
4k
views
Unramified extension of number fields
Any finite field extension (in particular Galois extension) of $\mathbb{Q}$ is ramified. Is there an intuitive geometric explanation of this fact?
Suppose we have an number field $K$, is any Galois e …
- 1,613
1
vote
2
answers
1k
views
Is the absolute Galois group the same as the automorphism group? [closed]
Is the absolute Galois group $\mathrm{Gal}(\overline{\mathbf{Q}}|\mathbf{Q})$ the same as the group $\mathrm{Aut}_{\mathbf{Q}}(\overline{\mathbf{Q}})$ the automorphism group in the category of $\mathb …
- 1,613
2
votes
0
answers
344
views
Automorphism group of $\mathbf{C}$ over $\overline{\mathbf{Q}}$
Choose an embedding $\overline{\mathbf{Q}}\rightarrow \mathbf{C}$ from an algebraic closure of the field of rationals to the field of complex numbers.
Question 1: Is it true that $\mathbf{C}$ is isom …
- 1,613