Timeline for How badly can strong multiplicity one fail in the theory of automorphic representations?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2011 at 20:11 | comment | added | Kevin Ventullo | Heh, yes I suppose that is an easier way of saying it. | |
| Sep 10, 2011 at 15:12 | comment | added | Kevin Buzzard | Oh -- you mean there's just one prime above $p$. Thanks for the clarification! | |
| Sep 10, 2011 at 8:38 | comment | added | Kevin Ventullo | Sorry, I'm not sure what to call it. I mean that the field can be written as $L>K>\mathbb{Q}$, where $p$ is totally ramified in $K/\mathbb{Q}$ and inert in $L/K$. | |
| Sep 10, 2011 at 8:02 | comment | added | Kevin Buzzard | Thanks -- this sounds like another reference for the "well-known" part. What does "some prime has no splitting" mean? | |
| Sep 9, 2011 at 21:02 | comment | added | Kevin Ventullo | In Example 3 on pg. 122 of Algebraic Groups and their Birational Invariants by Voskresenskii, there is an explicit description of a torus which does not satisfy "weak approximation." The example is $T=R^{(1)}_{L/\mathbb{Q}}(\mathbb{G}_m)$, where $R^{(1)}$ denotes the norm 1 elements of $\mathrm{Res}_{L/\mathbb{Q}}$, and $L$ is any biquadratic extension in which some prime has no splitting. | |
| Sep 8, 2011 at 16:34 | history | answered | Kevin Buzzard | CC BY-SA 3.0 |