Timeline for Do the absolute roots restricting to a given root form a Galois orbit?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 15, 2018 at 16:07 | comment | added | Not a grad student | @LSpice I think he was referring to Selbach. | |
| Nov 14, 2018 at 15:44 | comment | added | LSpice | @CoffeeBliss, for an example of the behaviour you describe, just compare the behaviour of a $k$-split maximal torus $T$ in $G$ (supposing for simplicity that one exists) to a non-$k$-split maximal torus $T'$, with $K$ the splitting field of $T'$. | |
| Nov 14, 2018 at 15:43 | comment | added | LSpice | @JimHumphreys, who is Tits's Bonn student? | |
| Aug 30, 2018 at 0:06 | history | edited | Jim Humphreys | CC BY-SA 4.0 |
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| Aug 22, 2018 at 17:58 | comment | added | Not a grad student | Thanks. For example, Borel-Tits write in section 6.2 that if K/k is a field extension, and T and T' are maximal K-split tori both invariant under Aut(K/k), then the usual Aut(K/k)-modules X^*(T) and X^*(T') need not be isomorphic. | |
| Aug 22, 2018 at 17:34 | comment | added | Jim Humphreys | @CoffeeBliss: Probably the best examples are found in the classification survey by Tits (in English) in the 1965 Boulder AMS proceedings volume. Though his theoretical formulation needed some tweaking later on (in the work of his Bonn student), his case-by-case study is quite useful. He also indicates what is true for various familiar types of fields. | |
| Aug 22, 2018 at 17:02 | comment | added | Not a grad student | What are some good examples to keep in mind when reading these sections? | |
| Aug 5, 2018 at 15:41 | history | answered | Jim Humphreys | CC BY-SA 4.0 |