Timeline for Question on definition of closed embedding of affine group schemes
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 19 at 6:40 | comment | added | Wilberd van der Kallen | @Melon_Musk Just delete 'group' and replace 'homomorphism' with 'morphism'. | |
| Sep 18 at 18:26 | comment | added | Melon_Musk | @WilberdvanderKallen Could you expand your comment? What exactly is the definition related to affine schemes? | |
| Sep 18 at 7:35 | comment | added | Wilberd van der Kallen | The main reason for the terminology is that this is the definition for affine schemes. One would not want a different meaning for affine group schemes. | |
| Sep 18 at 2:07 | comment | added | Christopher Drupieski | Perhaps if $B' = S^{-1}A$ is a localization of $A$, then the canonical map $\phi: A \to B'$ is an epimorphism of commutative rings (but not a surjective ring homomorphism), and then the corresponding map of affine schemes is a monomorphism? At any rate, this question could be relevant: What do epimorphisms of (commutative) rings look like? | |
| Sep 17 at 15:39 | history | edited | Melon_Musk | CC BY-SA 4.0 |
edited title
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| Sep 17 at 12:45 | history | edited | Melon_Musk | CC BY-SA 4.0 |
edited body
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| Sep 17 at 12:44 | comment | added | Melon_Musk | Yes yes, I messed up while writing. Edited now | |
| Sep 17 at 12:09 | history | edited | LSpice | CC BY-SA 4.0 |
Link to book
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| Sep 17 at 12:03 | comment | added | LSpice | I think your algebra map is the wrong way around: a map of schemes from $H'$ to $G$ should be a map of algebras from $A$ to $B'$, not $B'$ to $A$. \\ I don't know an example off the top of my head, but note that a closed embedding is not just an injection on the functorial level, but an isomorphism of $H'$ with a closed subgroup of $G$. | |
| Sep 17 at 12:01 | history | edited | LSpice | CC BY-SA 4.0 |
Tidying
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| Sep 17 at 11:39 | history | asked | Melon_Musk | CC BY-SA 4.0 |