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| The basic question was whether there is a ]: | The basic question was whether there is a ]: | ||
| :<math>A^*(X) \to \operatorname{H}^*(X, \mathbb{Z}).</math> | :<math>A^*(X) \to \operatorname{H}^*(X, \mathbb{Z}).</math> | ||
| If ''X'' is smooth, such a map exists since <math>A^*(X)</math> is the usual ] of ''X''. {{harv|Totaro|2014}} has shown that there might not be such a map even if ''X'' is a ], roughly a variety admitting a cell decomposition. He also notes Voevodsky’s motivic cohomology ring is "probably more useful " than the operational Chow ring |
If ''X'' is smooth, such a map exists since <math>A^*(X)</math> is the usual ] of ''X''. {{harv|Totaro|2014}} has shown that there might not be such a map even if ''X'' is a ], roughly a variety admitting a cell decomposition. He also notes Voevodsky’s ] is "probably more useful " than the operational Chow ring for a singular scheme (§ 8 of loc. cit.) | ||
| == References == | == References == | ||
Revision as of 05:12, 4 November 2015
The basic question was whether there is a cycle map:
If X is smooth, such a map exists since is the usual Chow ring of X. (Totaro 2014) harv error: no target: CITEREFTotaro2014 (help) has shown that there might not be such a map even if X is a linear variety, roughly a variety admitting a cell decomposition. He also notes Voevodsky’s motivic cohomology ring is "probably more useful " than the operational Chow ring for a singular scheme (§ 8 of loc. cit.)
is the usual References
- W. Fulton, R. MacPherson, F. Sottile, and B. Sturmfels, ‘Intersection theory on spherical varieties’, J. Alg. Geom. 4 (1995), 181–193.
- Totaro, Chow groups, Chow cohomology and linear varieties
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