Timeline for Weil restriction
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 25, 2014 at 15:57 | comment | added | user57473 | Ok, thanks! One last question: can the statement be made true (at least for some large "classes" of $G$, e.g. tori, etc) by adding further assumptions on $X$ and $Y$? | |
| Aug 25, 2014 at 15:49 | history | edited | Jason Starr | CC BY-SA 3.0 |
added 20 characters in body
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| Aug 25, 2014 at 15:49 | comment | added | Jason Starr | It is still false, for instance, if $k$ equals $\mathbb{Q}$, if $X$ equals $\text{Spec}(\mathbb{Q})$, if $Y$ equals $\text{Spec}(\mathbb{Q}[i])$, and if $G$ equals $\mathbb{G}_m$. Since you can get the previous counterexample from this one by basechange, there cannot be an isomorphism. | |
| Aug 25, 2014 at 15:45 | comment | added | user57473 | (This is still user57469, I had to reboot my laptop and for some reason I'm not logged in anymore.) Is the statement false if we specialize $k$ to e.g. a number field? If the general statement is still false even in this more restricted setting, is there any well-known case when the statement holds (some guesses: $G$ a torus or maybe $G$ just connected)? | |
| S Aug 25, 2014 at 15:36 | history | answered | Jason Starr | CC BY-SA 3.0 | |
| S Aug 25, 2014 at 15:36 | history | made wiki | Post Made Community Wiki by Jason Starr |