 | 1 | initial version |
Say I want to look at the field extension $Quot(\mathbb{Q}[x,y]/y^7-x)$ over $\mathbb{Q}(x)$ and then compute its Galois closure. How do I do that?
Ideally it could be done on the scheme-level (to define the scheme-morphism: (the projectivization of the affine plane curve $y^7-x$) mapping to (the projective $x$-line); and then compute its Galois closure -- a scheme!). But I don't know how to implement either version.
| | 2 | No.2 Revision |
Say I want to look at the field extension $Quot(\mathbb{Q}[x,y]/y^7-x)$ over $\mathbb{Q}(x)$ and then compute its Galois closure. How do I do that?
Ideally it could be done on the scheme-level (to define the scheme-morphism: (the projectivization of the affine plane curve $y^7-x$) mapping to (the projective $x$-line); and then compute its Galois closure -- a scheme!). But I don't know how to implement either version.
| | 3 | retagged |
Say I want to look at the field extension $Quot(\mathbb{Q}[x,y]/y^7-x)$ over $\mathbb{Q}(x)$ and then compute its Galois closure. How do I do that?
Ideally it could be done on the scheme-level (to define the scheme-morphism: (the projectivization of the affine plane curve $y^7-x$) mapping to (the projective $x$-line); and then compute its Galois closure -- a scheme!). But I don't know how to implement either version.
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