Timeline for critical values of motives
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 22, 2013 at 8:34 | comment | added | François Brunault | I'm not an expert but I think these cases have been completely classified, see the recent work of Schütt and Elkies-Schütt. | |
| Mar 21, 2013 at 19:46 | comment | added | critval | Yes, $h^2(X)$ decomposes as $\mathbb{L}^\rho \oplus t(X)$ where $\rho$ is the Picard number of $X$ and you want to consider the submotive $t(X)$. Do you have references for the cases you mention? Are there such examples for $\rho<20$? Thanks | |
| Mar 21, 2013 at 19:33 | comment | added | François Brunault | I'm not sure, but when $X$ is a K3 surface the motive $M=h^2(X)$ has rank 22 and there are many trivial Euler factors so you may want to consider a direct factor of $M$ instead. The only cases I know of give you a motive of the form $M(f)$ where $f$ is a newform of weight 3. This is a rank 2 motive whose critical integers are only $s=1,2$. In this case the functional equation relates $L(f,s)$ and $L(f,3-s)$. | |
| Mar 21, 2013 at 17:55 | comment | added | critval | Merci François! Do you have an idea of how to compute the action of complex conjugation on $H^{1,1}$ of a K3 surface, at least in some examples? | |
| Mar 21, 2013 at 15:50 | history | answered | François Brunault | CC BY-SA 3.0 |