| Revision as of 22:57, 24 September 2019 editHasteur (talk | contribs)31,857 editsm Reverted 1 edit by TakuyaMurata (talk) to last revision by Hasteur (TW)Tags: New redirect Undo← Previous edit | Revision as of 22:59, 24 September 2019 edit undoTakuyaMurata (talk | contribs)Extended confirmed users, IP block exemptions, Pending changes reviewers89,986 edits Undid revision 917677289 by Hasteur (talk) umm, this is just editing warringTags: Removed redirect UndoNext edit → | ||
| Line 1: | Line 1: | ||
| {{mfd-mergeto|Chow group|Draft:Operational Chow ring|9 March 2018|Talk:Chow group}} | |||
| #REDIRECT ] | |||
| The basic question was whether there is a ]: | |||
| {{r to section}} | |||
| :<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 rationally there is no such a map with good properties even if ''X'' is a ], roughly a variety admitting a cell decomposition. He also notes that Voevodsky’s ] is "probably more useful " than the operational Chow ring for a singular scheme (§ 8 of loc. cit.) | |||
| == References == | |||
| *W. Fulton, R. MacPherson, F. Sottile, and B. Sturmfels, ‘Intersection theory on spherical varieties’, J. Alg. Geom. 4 (1995), 181–193. | |||
| *Totaro, | |||
| {{geometry-stub}} | |||
Revision as of 22:59, 24 September 2019
 | This page was nominated for deletion. The debate was closed on 9 March 2018 with a consensus to merge the content into the page Chow group. If you find that such action has not been taken promptly, please consider assisting in the merger instead of re-nominating the page for deletion. To discuss the merger, please use the destination page's talk page. |
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 rationally there is no such a map with good properties even if X is a linear variety, roughly a variety admitting a cell decomposition. He also notes that 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
 | This geometry-related article is a stub. You can help Misplaced Pages by expanding it. |