Timeline for Independence of $\ell$-adic homological equivalence of $\ell$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2017 at 19:27 | comment | added | SashaP | mathoverflow.net/questions/223975/… | |
| Apr 29, 2017 at 18:20 | comment | added | R. van Dobben de Bruyn | Also, in characteristic $0$ the result with $\mathbb Q_\ell$-coefficients is known unconditionally, by comparison with singular cohomology. An unconditional proof in characteristic $p > 0$ would be very interesting; this is not known. | |
| Apr 29, 2017 at 18:11 | comment | added | R. van Dobben de Bruyn | This has to do with torsion in $\operatorname{Pic}/\operatorname{Pic}^0$. The torsion is finitely generated, so some primes do and some do not occur in it. | |
| Apr 29, 2017 at 12:03 | comment | added | Piotr Achinger | The canonical divisor of an Enriques surface is $2$-torsion (at least if ${\rm char}(k)\neq 2$), so it is $\mathbf{Z}_2$-homologically nontrivial but $\mathbf{Z}_\ell$-homologically trivial for $\ell\neq 2$. With $\mathbf{Q}_\ell$ coefficients, such an example would contradict the Standard Conjecture D. | |
| Apr 29, 2017 at 11:42 | history | asked | pi_1 | CC BY-SA 3.0 |