Timeline for Motive of CM elliptic curve and modular forms
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 18, 2022 at 18:28 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
a minor typo
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| May 18, 2022 at 18:27 | history | edited | LSpice | CC BY-SA 4.0 |
Link to Rohrlich article, while this is on the front page
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| May 18, 2022 at 18:27 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
a minor typo
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| Jun 8, 2013 at 8:03 | comment | added | cmotive | So where is this CM expert? :) | |
| Jun 6, 2013 at 19:34 | comment | added | François Brunault | I once saw a result stating that the Hecke correspondences generate the whole endomorphism algebra of the Jacobian of a modular curve, so the answer should be yes, but I don't recall the reference. | |
| Jun 6, 2013 at 19:22 | comment | added | François Brunault | This is a good question -- on the Galois side, the Galois representations associated to $f$ and $A_f$ decompose into two rank 1 pieces after restricting to the absolute Galois group of the imaginary quadratic field $F$ by which $E$ has CM. These pieces are cut out by the endomorphisms of $E$ which are not defined over $\mathbf{Q}$, and we may wonder whether these endomorphisms are modular i.e. are induced by some Hecke correspondences on modular curves above $f$. I think this should be true at least in some cases, but I'm not sure and I hope an expert of the CM case can show up. | |
| Jun 6, 2013 at 18:48 | comment | added | cmotive | Thanks for your answer, François! Do you know something about the second question, that is, how to see the two submotives of rank one in $A_f$? | |
| Jun 6, 2013 at 17:08 | history | edited | François Brunault | CC BY-SA 3.0 |
Added condition on K; added 11 characters in body
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| Jun 6, 2013 at 17:00 | history | answered | François Brunault | CC BY-SA 3.0 |