Timeline for Does there exist a functorial splitting for the weight filtration (of singular cohomology)?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Nov 21, 2010 at 0:24 | comment | added | Mikhail Bondarko | An observation on elliptic curves over finite fields (that fails over infinite ones): all points are torsion all curves have complex multiplication. | |
| Nov 21, 2010 at 0:19 | comment | added | Mikhail Bondarko | Dear Donu, I will certainly be very glad to get an e-mail from you, and will write you if I will have anything big on the subject. | |
| Nov 20, 2010 at 23:44 | history | edited | Donu Arapura | CC BY-SA 2.5 |
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| Nov 20, 2010 at 23:37 | comment | added | Donu Arapura | OK, I see. I realize that I was probably hasty in the way I set up my example, since Hodge theoretic (and presumably Galois theoretic) extension class corresponding to $$0\to {\mathbb Q}(1)\to H_1(E-\{p,q\})\to H_1(E)\to 0$$ vanishes because p and q are linearly equivalent. Let me try again with E any curve with involution such that $E/\sigma$ has positive genus. Although I should probably work it out carefully. By the way, it may be more efficient to communicate by email. It would be nice to get this example sorted out. | |
| Nov 20, 2010 at 23:00 | comment | added | Mikhail Bondarko | I am sorry; could you explain the second to last statement? This seems a bit strange: similar arguments should work for an elliptic curve over a finite field, yet in this case there exists a canonical splitting for the filtration. | |
| Nov 20, 2010 at 19:15 | history | edited | Donu Arapura | CC BY-SA 2.5 |
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| Nov 20, 2010 at 19:02 | history | answered | Donu Arapura | CC BY-SA 2.5 |