Timeline for representations of an algebraic group and extension of scalars
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2017 at 8:02 | vote | accept | exty | ||
| Dec 23, 2017 at 6:00 | comment | added | nfdc23 | @JulianRosen: Oh, good point. I'm still pretty sure that for general unipotent $K$-groups (say in characteristic 0) the essential surjectivity does fail, but I'd need to think it through some more, on another day. | |
| Dec 23, 2017 at 5:58 | comment | added | nfdc23 | @მამუკაჯიბლაძე: Your first question is affirmative under the hypotheses of the Theorem above, and the second is "trivially yes" since field extensions are faithfully flat (though of course one doesn't need the notion of faithful flatness to see this, just some bases). | |
| Dec 23, 2017 at 5:48 | comment | added | მამუკა ჯიბლაძე | So $(-)_{K'}$ is bijective on isomorphism classes of objects? Is it faithful? (Clearly it is not full in all nontrivial cases) | |
| Dec 23, 2017 at 5:28 | comment | added | Julian Rosen | An issue with Ext groups is that two non-isomorphic extensions can be isomorphic as representations. As an example, I believe the functor is essentially surjective for the unipotent group $\mathbb{G}_a$, even though the map on Ext groups is not surjective. | |
| Dec 23, 2017 at 4:50 | history | edited | nfdc23 | CC BY-SA 3.0 |
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| S Dec 23, 2017 at 4:32 | history | answered | nfdc23 | CC BY-SA 3.0 | |
| S Dec 23, 2017 at 4:32 | history | made wiki | Post Made Community Wiki by nfdc23 |