Talk:Motive (algebraic geometry)

From Wikipedia, the free encyclopedia

Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	B Class	High Priority	Field: Geometry
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. needs more on the relation to algebraic K-theory Jakob.scholbach 00:34, 22 April 2007 (UTC)

Note about wikifying mathematicians. I firstly wikified those who I considered important according to my mathematical taste. It happened to agree with Fields medal. ilya 01:22, 15 Jan 2004 (UTC)

[edit] References

This article needs specific references cited, not just external links. Is it original research?

Lmcelhiney 06:59, 24 December 2006 (UTC)

I've rewritten the article and added references. I did not add references for each theorem, definition etc., but the references do cover all of the material and I tried to specify which part they cover. Also, it is not original research. Jakob.scholbach 01:57, 31 March 2007 (UTC)

[edit] Algebraic cycles

I think at least some of the material on algebraic cycles should be moved to that article. The discussion of the 'standard conjectures' really belongs there (the implications for motives should stay here). Also, some of the discussion of equivalence relations for algebraic cycles should probably be moved out: its importance is not limited to the topic of motives at all. Charles Matthews 21:25, 3 April 2007 (UTC)

Yes. Let's do that. I guess the mathematical organization is: 1. algebraic cycles, 2. equivalence relations, 3. Weil cohomology theories, 4. standard conjectures (they are not only about cycles, but do involve the W.c.t.). 5. motives. Perhaps it's best to have separate articles for all of these points. I will also try to minimize-eliminate the current vague style in the article of algebraic cycles. On the other hand, at least for me personally, the motivic interpretation of the standard conjectures is the most neat one and so probably also some considerable part of the conjectures should remain in this article. Jakob.scholbach 03:46, 4 April 2007 (UTC)

The vagueness is related to my not having thought about these things since the early 1980s ... Charles Matthews 21:37, 5 April 2007 (UTC)

No problem; I didn't mean to criticize you. I provided a definition there and wrote also something about intersection products (see intersection theory). I'll also write a bit on Weil cohomology theories and take the material from the last section in algebraic cycles there. Jakob.scholbach 00:52, 8 April 2007 (UTC)