Timeline for complex multiplication
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 11, 2012 at 7:28 | comment | added | user29720 | @unknown: reference for which? I mentioned a couple of things. | |
| Dec 11, 2012 at 6:53 | comment | added | user565739 | @kreck, I felt strange that it is written that "...be a quaternion algebra over a quadratic field...". It is good to know that it contains an imaginary quadratic field and the theorem Tate proved. Could you give the reference for it. Thank you very much. | |
| Dec 11, 2012 at 6:43 | comment | added | user29720 | @stankewicz: Tate proved that abelian varieties over finite fields always have complex multiplication over the ground field (in the sense of the endomorphism algebra over the ground field containing a CM algebra of rank twice the dimension, where "CM algebra" means "product of CM fields"). @unknown: That link is wrong: the endomorphism algebra of a ss elliptic curve over an alg. closed field is of rank at most 4, so it cannot be a quaternion algebra over a quadratic field. It is just a quaternion algebra over $\mathbf{Q}$ and contains an imaginary quadratic field (even infinitely many). | |
| Dec 10, 2012 at 21:00 | answer | added | anon | timeline score: 3 | |
| Dec 10, 2012 at 20:30 | history | edited | user565739 | CC BY-SA 3.0 |
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| Dec 10, 2012 at 20:26 | comment | added | stankewicz | Most people, include as a definition of complex multiplication that your abelian variety is defined over a field of characteristic zero. | |
| Dec 10, 2012 at 20:06 | history | edited | user565739 | CC BY-SA 3.0 |
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| Dec 10, 2012 at 19:58 | history | edited | user565739 | CC BY-SA 3.0 |
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| Dec 10, 2012 at 19:50 | history | asked | user565739 | CC BY-SA 3.0 |