Timeline for modularity of algebraic varieties
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| May 11, 2010 at 4:23 | vote | accept | Nicolás | ||
| May 11, 2010 at 1:00 | history | edited | user1594 | CC BY-SA 2.5 |
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| May 11, 2010 at 0:54 | comment | added | user1594 | Thanks! There are two reasons why the K3 surfaces above might not be "satisfactory": first, the motive of a K3 surface embeds always in the motive of an abelian variety (possibly of much higher dimension). Second, the only interesting part of the cohomology of the singular K3 surfaces is the transcendental cycles, and the theorem of Livné I mentioned above says that this comes from CM eigenforms - these are less "interesting" than other Galois representations you might find out there. | |
| May 10, 2010 at 23:10 | comment | added | Pete L. Clark | ...and good enough for an answer: +1. I would say that these K3 surfaces are "not Shimura varieties" in the sense that they are not constructed from a "Shimura datum" via the Shimura-Deligne construction. As to whether they are isomorphic to Shimura varieties: probably some of them are but "most" of them are not. But it may not be easy to point to a specific example. | |
| May 10, 2010 at 19:44 | history | answered | user1594 | CC BY-SA 2.5 |