Timeline for Integral decomposition of the diagonal (Chow motives)
Current License: CC BY-SA 2.5
4 events
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| Apr 15, 2011 at 23:51 | comment | added | SGP | even over an algebraically closed field, this may not hold in general. See for instance, the examples of Janos Kollar: if $X$ is a general hypersurface of degree $3m^2$ in projective space (and $(6,m) =1)$), then the class of every curve on $X$ is $m$-times the class of a line. Kollar's result is referred to here www.math.ist.utl.pt/geometry09/kollar.pdf | |
| Oct 25, 2010 at 9:23 | comment | added | Xandi Tuni | True, I should have asked this for $k$ algebraically closed. Conic with no rational points = Conic with no 0-cycle of degree 1, so $h^0$ doesn't split off. | |
| Oct 23, 2010 at 10:45 | comment | added | Tony Scholl | I will write something longer if I get a chance, but one thing to say is that if $k$ is not algebraically closed there are simple counterexamples - take $X$ to be a conic with no points. | |
| Oct 23, 2010 at 10:01 | history | asked | Xandi Tuni | CC BY-SA 2.5 |