Draft talk:Geometric Mixed-Motives

Rejection and Notability
I'm not sure why this article was rejected. The sources are scholarly articles!


 * You should not submit the draft to the AfC, which is a broken process. Please seek an assistant at WikiProject Mathematics instead. -- Taku (talk) 20:21, 12 September 2017 (UTC)
 * How can I ask for help/find an assistant?
 * Start a new section at Wikipedia talk:WikiProject Mathematics and then asks whether any registered user is willing to move the draft to the mainspace. This way, unlike the AfC, the draft gets reviewed by someone with mathematical backgrounds. -- Taku (talk) 04:32, 17 September 2017 (UTC)

Todo

 * List properties these motives have
 * Give example computations with these properties with cohomological realizations
 * includes Gysin morphisms
 * includes blowups
 * Discuss the relation with effective chow motives
 * Embed geometric category into etale motives and nisnevich motives.

A new article is not needed
Here are some comments showing that the rejection of the article creation was justified, independently of the notability of the sources.
 * Wikipedia has an article Motive (algebraic geometry). This article is not linked to in the draft
 * You should see the discussion on that page. Since there are many different theories for what mixed motives should be, there should be separate pages for each. — Preceding unsigned comment added by 128.138.65.89 (talk • contribs)


 * The second sentence of this article seems in contradiction with the content of the draft. Thus Motive (algebraic geometry) must been updated before creating the draft.
 * This is not a contradiction. If you look at other theories of mixed motives, the geometric mixed motives more closely resemble Grothendieck's original category of pure motives. — Preceding unsigned comment added by 128.138.65.89 (talk • contribs)


 * The draft lacks of context explaining to a non-specialist how this theory improves the theory of motives (Motive (algebraic geometry) is also weak from this point of view)
 * I can update this. — Preceding unsigned comment added by 128.138.65.89 (talk • contribs)


 * The length of the draft, and the preceding issues suggest that a new section in Motive (algebraic geometry) would better than a new article.
 * I plan on adding more content, see the todo list. — Preceding unsigned comment added by 128.138.65.89 (talk • contribs)

Some advices for the creator of the draft D.Lazard (talk) 18:36, 19 September 2017 (UTC)
 * Read WP:Five Pillars and WP:What Wikipedia is not
 * Start editing existing articles before creating new articles


 * I agree with 128. that Voevodsky's category of motives deserves an article on its own, whereas Motive (algebraic geometry) would ideally be hosting a comparison of different categories and notions of motives.
 * One advice I would like to offer at this point is not to address the reader. Unlike in usual mathematical writing, "we" and "note that" are frowned upon in Wikipedia articles, see WP:WE and WP:YOU for related information. Jakob.scholbach (talk) 07:09, 21 September 2017 (UTC)


 * I think the concern here is we don't want to have too many separate articles on each different theories (since we don't know which one is going to be important or to be in the main use). I don't have enough backgrounds in this area and so I'm neutral but Voevodsky's theory does seem prominent, judging from Google searches. My impression is no doubt biased by the statues of Voevodsky; but that may not be a wrong bias. While scientific works should speak themselves regardless of the creators, at least in Wikipedia (and often in the public in general), we take the works of prominent mathematicians more seriously. This one might be the case. (Personally I would just go with Jakob's judgement.) -- Taku (talk) 00:53, 23 September 2017 (UTC)


 * Berry Mazur expects that "The quest for a full theory motives is a potent driving force in complex analysis, algebraic geometry, automorphic representation theory, the study of L functions, and arithmetic. It will continue to be so, throughout the current century."


 * No, no, the question is whether this one particular theory is prominent/notable enough to deserve a separate article. The question can be approached non-mathematically or mathematically. Non-mathematically, this can be done for example by citing a survey-type article or book (as Lazard already explained). Mathematically, is there any reason this approach is somehow special; it stands out among other approaches? -- Taku (talk) 23:02, 23 September 2017 (UTC)


 * Maybe you're right. Here are two options I see: one is to create a page dedicated to the various Voevedsky motives, starting with geometric mixed motives and then constructing Nisnevich sheaves with transfers. Another option is to migrate the material from this page onto the motives page. What are people's thoughts?


 * (unindent) @Taku: Voevodsky's category of motives is certainly one of the most widely used category of motives. While we do have other categories, especially when it comes to motives over more general base schemes, Voevodsky's category continues to be highly important; much more than, say, the category of Chow motives which IMO has a primarily historic relevance. (The latter category is dealt with in detail on the motives article.) Jakob.scholbach (talk) 07:48, 25 September 2017 (UTC)
 * @anonymous editor: please sign your posts using 4 tildes ( ~ ) so that we can distinguish more easily the posts. Thanks! Jakob.scholbach (talk) 07:48, 25 September 2017 (UTC)
 * I don't have a strong opinion whether this should be merged into the main article. In the main article, we do have a short summary of the construction of Voevodsky's category, which is roughly the same as what is in the draft right now. If I were to work on the articles on motives on Wikipedia I would probably start by cleaning up the main article. Jakob.scholbach (talk) 08:14, 25 September 2017 (UTC)


 * I'm not sure if I agree with the opinion on Chow motive. By "motive", I have an impression people mean Chow motive; see a paer like https://arxiv.org/pdf/math/0007043.pdf (this area is closer to my research area.) -- Taku (talk) 00:36, 28 September 2017 (UTC)

Migrated
I have migrated this page to the main motives page Username6330 (talk) 01:09, 26 September 2017 (UTC)
 * And I have turned the page into a redirect so the history can be preserved. Hasteur (talk) 15:40, 27 September 2017 (UTC)