Timeline for Overview of automorphic representations for $SL(2)/{\mathbf{Q}}$?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Nov 30, 2009 at 0:53 | comment | added | moonface | I agree with you, but couldn't see it either; the "vanishing" was the best I could do. Here's an interesting case which might be helpful to think about: Consider $SL_2$ over a real quadratic field $F$. It gives us some complex two-dimensional (Hilbert modular) variety. In this case, an elliptic curve over $F$ would contribute four dimensions to the $H^2$, one dimension in Hodge numbers $(0,2),(2,0)$ and two dimensions in Hodge number $(1,1)$. A CM elliptic curve only contributes half of this. What's going on in direct terms? I couldn't see this. | |
| Nov 29, 2009 at 22:55 | vote | accept | Kevin Buzzard | ||
| Nov 29, 2009 at 22:54 | comment | added | Kevin Buzzard | Thanks. Yes I know about the "other" $SL_n$ phenomenon: there is a paper by Erez Lapid that takes Blasius' work even further. What is irking me a little about $SL_2$ is that my gut feeling is that this "not every element of the packet is automorphic" phenomenon should perhaps manifest itself in a completely classical way when considering cuspidal modular forms with only the Hecke operators coming from SL_2: the CM forms should perhaps behave differently, But somehow I don't see it. Maybe I am still not quite seeing what's truly happening. Thanks for the very informative answer though. | |
| Nov 29, 2009 at 1:09 | history | answered | moonface | CC BY-SA 2.5 |