Timeline for Reference for Rationality in Algebraic Groups in the Language of Schemes?
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Apr 27, 2013 at 17:32 | comment | added | user1437 | @ayanta: thank you for the references, I'll take a look. @Kidwell: I have taken a look at B. Conrad's notes from his course now and these are essentially the kind of thing I want. If you post your comment as an answer, I shall accept it. @Putman: Thank you also for the link; the notes look promising as well, and I'll keep an eye out for their progress. | |
| Apr 27, 2013 at 16:25 | comment | added | user30180 | @Jason: The existence of the split form (usually called the Existence Theorem) is proved in those Luminy notes over $\mathbf{Z}$. The existence and uniqueness of a quasi-split inner form is also treated there, in the cohomological exercises. | |
| Apr 27, 2013 at 16:19 | comment | added | user1437 | @ayanta: yes sorry, I was being sloppy. I am aware that not all groups are split or quasisplit. The result on the existence of split and quasisplit forms is one thing for example that I‘d like to see. @Kidwell: thanks, I will take a look at these notes! | |
| Apr 27, 2013 at 13:37 | comment | added | user30180 | What do you mean by "(such as existence of....Borel subgroups defined over the base field)"? There are plenty of examples that have no Borel subgroup over the ground field (i.e., are not quasi-split). Do you mean rational conjugacy of minimal parabolics, that every connected reductive group has a unique quasi-split inner form, or something else? | |
| Apr 27, 2013 at 2:49 | comment | added | Andy Putman | They're not yet complete, so I don't know if they will eventually have everything you want, but Milne is in the process of writing a long book on algebraic groups from the perspective of group schemes. My impression is that he wants to do the stuff that Borel does (+ more) from a modern perspective. What's written is here : jmilne.org/math/CourseNotes/ala.html | |
| Apr 27, 2013 at 2:18 | comment | added | Keenan Kidwell | Have you looked at the notes from Brian Conrad's courses on linear algebraic groups? They are of course thoroughly modern. In particular, there are course notes covering the entirety of the first semester which might have some of what you want. | |
| Apr 26, 2013 at 23:04 | history | edited | user1437 | CC BY-SA 3.0 |
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| Apr 26, 2013 at 22:57 | history | asked | user1437 | CC BY-SA 3.0 |