Timeline for Elementary reference for algebraic groups
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Aug 11, 2018 at 2:18 | history | edited | Martin Sleziak |
added (textbook-recommendation) tag
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| Sep 29, 2010 at 16:35 | comment | added | Jim Humphreys | For discussion of Jordan decomposition in linear algebraic groups, look at the earlier MO post #30042 from June 30. | |
| Sep 29, 2010 at 5:27 | comment | added | David Corwin | @Jim: Could you please provide a reference? | |
| Sep 29, 2010 at 5:11 | answer | added | Victor Protsak | timeline score: 3 | |
| Sep 28, 2010 at 18:45 | answer | added | Mikhail Borovoi | timeline score: 6 | |
| Sep 28, 2010 at 17:43 | comment | added | Jim Humphreys | I have to recuse myself from this question, having written an exposition of the Borel/Bass lecture notes in my carefree (and tenure-free) youth. All books mentioned here are useful, but for varied purposes and using geometry at different levels. One concrete early motivation for the algebraic group mixture of group theory and algebraic geometry is the Kolchin-Borel-Chevalley work showing the intrinsic nature of the multiplicative Jordan decomposition. This is elementary (albeit technical) but not conceptually obvious. Quotients and such get far more sophisticated. | |
| Sep 28, 2010 at 8:13 | answer | added | Bugs Bunny | timeline score: 3 | |
| Sep 28, 2010 at 2:43 | answer | added | Andy Putman | timeline score: 3 | |
| Sep 28, 2010 at 2:23 | answer | added | Christopher Drupieski | timeline score: 8 | |
| Sep 28, 2010 at 2:04 | comment | added | BCnrd | Milne has lectures notes which are probably excellent (I haven't looked at them). Whatever you read, the beef is str. theory of reductive alg. gps. In absence of schemes, some things in char. $> 0$ are a bit clunky in comparison with char. 0 because kernels can be non-smooth; e.g., ${\rm{SL}}_p \rightarrow {\rm{PGL}}_p$ in char. $p > 0$ with "kernel" $\mu_p$, akin to purely insep. isogeny of ell. curves. When you learn schemes and sheaves, some awkward things with quotients and non-smooth subgroups (and centralizers, and center, and so on) in char. $> 0$ will become more straightforward. | |
| Sep 28, 2010 at 1:26 | answer | added | Peter Arndt | timeline score: 10 | |
| Sep 28, 2010 at 1:15 | answer | added | Chuck Hague | timeline score: 14 | |
| Sep 28, 2010 at 1:00 | history | asked | David Corwin | CC BY-SA 2.5 |