Timeline for Construction of abelian varieties from Hilbert modular forms?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Feb 8, 2011 at 8:33 | comment | added | jvo | @David Hansen: Thanks for pointing this out! | |
| Feb 8, 2011 at 8:33 | comment | added | jvo | @Barry Lyndon: Oh, I see. I had been wondering why no one seems to work directly with Hilbert modular varieties in these constructions ... I suppose this also explains the importance of Jacquet-Langlands correspondence (to reduce to the study of Shimura curves) in the work of Carayol and others. Thanks for pointing this out. | |
| Feb 7, 2011 at 22:11 | comment | added | David Hansen | @vo: Hilbert modular varieties don't have Jacobians, they have Albaneses, and these tend to be trivial! | |
| Feb 7, 2011 at 8:32 | comment | added | jvo | Thanks for this reply, this is exactly the kind of answer I was looking for! Incidentially, on the topic of conditions imposed by Shimura curves, does the analogous construction via Hilbert modular varieties not work too? That is, start with a Hilbert modular eigenform of parallel weight 2, viewed as a function on some associated Hilbert modular variety Y which equipped with an algebra of Hecke correspondences. Let J be the jacobian of Y, with T the subalgebra of $\End(J)$ generated by Hecke correspondences. The eigenform gives rise to a homomorphism as above, with kernel $I$. Let $A=J/I$? | |
| Feb 7, 2011 at 8:23 | vote | accept | jvo | ||
| Feb 6, 2011 at 22:23 | history | answered | user631 | CC BY-SA 2.5 |