Timeline for higher direct image, Shimura varieties of PEL-type and representations
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 26, 2011 at 13:50 | comment | added | Przemyslaw Chojecki | See the article of Saito, which I have mentioned above: he defines by a representation of $G^c$ in (4.8) a local system $\mathcal{F} ' _l$ (if you complexify this, you'll get an automorphic vector bundle) and later on, in the beginning of section 6.1, he claims that $R^1 a_ \mathbb{Q} _l = \mathcal{F} ' _l$ | |
| May 26, 2011 at 13:47 | comment | added | Przemyslaw Chojecki | See the article of Saito, which I have mentioned above: he defines by a representation of $G^c$ in (4.8) a local system $\mathcal{F} ' _l$ (if you complexify this, you'll get an automorphic vector bundle) and later on, in the beginning of section 6.1, he claims that $R^1 a_* \mathbb{Q} _l = \mathcal{F} ' _l$. | |
| May 19, 2011 at 20:39 | comment | added | Keerthi Madapusi | You might want to look at this question: mathoverflow.net/questions/25354/… | |
| May 19, 2011 at 20:36 | comment | added | Keerthi Madapusi | The higher push-forwards you're concerned with are $l$-adic local systems. They cannot directly be expressed in terms of vector bundles. What is possible is to look at the associated complex local systems and study them using Hodge theory. It is here that the automorphic vector bundles make an appearance, though there are additional issues when $M$ is not compact. | |
| May 19, 2011 at 14:07 | history | asked | Przemyslaw Chojecki | CC BY-SA 3.0 |