Timeline for Is the union of Cartan subgroups over $k$ dense?
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5 events
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| May 20, 2011 at 17:25 | comment | added | Jim Humphreys |
Concerning the accepted answer and the newer proposed one, the key point is just the finiteness of the number of maximal tori defined over $k$ (so their union is closed and of dimension equal to the rank of $G$): in concrete terms, such a torus is the zero set in $G$ of finitely many polynomials with coefficients in $k$. For more detailed discussion see for instance the Springer-Steinberg article (section II.1) in the 1970 Lect. Notes in Math. 131 (Springer).
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| May 6, 2011 at 22:45 | comment | added | Jim Humphreys | The Tohoku paper by Borel and Springer (1968) is valuable for its treatment of finer points about rationality properties of linear algebraic groups and their Lie algebras which don't usually fit into textbooks. It's actually part II of a paper for which part I appears in the proceedings (1966) of the 1965 AMS Summer Institute in Boulder. Part II, including generation of a connected reductive group over a finite field by maximal tori defined over that field (a nontrivial result), is based partly on older work by Rosenlicht and then Grothendieck but doesn't use scheme language explicitly. | |
| May 6, 2011 at 13:18 | vote | accept | Sophi | ||
| May 6, 2011 at 11:44 | answer | added | Laurent Moret-Bailly | timeline score: 6 | |
| May 6, 2011 at 11:21 | history | asked | Sophi | CC BY-SA 3.0 |