Timeline for Injection of $G(k)/Z(k)$ into $(G/Z)(k)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 11 at 6:24 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Apr 10 at 23:41 | comment | added | Kenta Suzuki | To elaborate on YCor's comment: $1\to Z(k^{sep})\to G(k^{sep})\to G^{ad}(k^{sep})\to 1$ is an exact sequence, and taking $\mathrm{Gal}(k^{sep}/k)$-fixed points is a left exact functor. | |
| Apr 10 at 21:48 | comment | added | YCor | For $k$ algebraically closed it's a bijection (I guess, essentially by definition of quotient). Injectivity follows for arbitrary fields. | |
| Apr 10 at 21:34 | history | edited | Μάρκος Καραμέρης | CC BY-SA 4.0 |
added link
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| Apr 10 at 21:29 | history | asked | Μάρκος Καραμέρης | CC BY-SA 4.0 |