Misplaced Pages

Draft:Operational Chow ring

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.

This is an old revision of this page, as edited by JJMC89 (talk | contribs) at 05:33, 9 September 2018 (G13). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Revision as of 05:33, 9 September 2018 by JJMC89 (talk | contribs) (G13)(diff) ← Previous revision | Latest revision (diff) | Newer revision → (diff)
This redirect may meet Misplaced Pages's criteria for speedy deletion as either a page in the draftspace, a declined/unsubmitted userspace Articles for Creation page, or a draft in either namespace with no content except the placeholder article wizard text that has not been edited (excluding bot edits) in over six months. See CSD G13.%5B%5BWP%3ACSD%23G13%7CG13%5D%5D%3A+Abandoned+draft+or+%5B%5BWikipedia%3AArticles+for+creation%7CAfC%5D%5D+submission+%E2%80%93+If+you+wish+to+retrieve+it%2C+please+see+%5B%5BWP%3AREFUND%2FG13%5D%5DG13

If this redirect does not meet the criteria for speedy deletion, please remove this notice.

This draft was nominated by JJMC89 on September 9, 2018.
It MAY qualify to be deleted per WP:CSD#G13 as the edit before that occurred on September 9, 2018 (6.35 years ago).If you plan to improve this draft, simply edit this page and remove the {{Db-afc}}, {{Db-draft}}, or {{Db-g13}} code.
Administrators: check links, talk, history (last), and logs before deletion.
This page was last edited by JJMC89 (contribs | logs) at 05:33, 9 September 2018 (UTC) (6 years ago)
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:

A ∗ ( X ) → H ∗ ⁡ ( X , Z ) . {\displaystyle A^{*}(X)\to \operatorname {H} ^{*}(X,\mathbb {Z} ).}

If X is smooth, such a map exists since A ∗ ( X ) {\displaystyle A^{*}(X)} 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.)


References

Stub icon

This geometry-related article is a stub. You can help Misplaced Pages by expanding it.