Talk:Nonabelian Hodge correspondence
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rename this page
editI think either this should be renamed or there should be a separate page with the title "Nonabelian Hodge correspondence" about the correspondence proved in general by Corlette and Simpson, between polystable Higgs bundles (with vanishing Chern classes) and semisimple representations of the fundamental group (of a smooth projective variety). On compact Riemann surfaces it was proved earlier by Hitchin and Donaldson (in rank 2). Its seems bizarre to delete the name of Corlette since he proved half the correspondence (see the statement of Theorem 1 in Simpson's ICM talk). One could then add a section at the bottom of this page that explains that Simpson extended this correspondence to include all semistable Higgs bundles, not just polystable ones (by looking at extensions). I am aware that various p-adic people use the name "Simpson correspondence", but they do not say why they delete the name Corlette.
Here is the link to Corlette's page on the list of "Mathematicians of the African diaspora": http://www.math.buffalo.edu/mad/PEEPS/corlette_kevin.html — Preceding unsigned comment added by 91.160.144.164 (talk) 16:43, 27 July 2020 (UTC)
- I am not an expert proper in this area, so I don't have a strong opinion. That said, what I see from glancing at various references is, that Corlette's input in this area is clearly acknowledged in many papers on the topic. However, a name such as "Simpson-Corlette correspondence" or "Corlette-Simpson c." is not used in the literature, so I believe it amounts (to some extent) to WP:OR to use that name for the article. The name "Nonabelian Hodge correspondence" is used, albeit a lot less frequently than "Simpson correspondence". Since I have not had a similar situation before, I will post a message on WT:WPM in order to collect some more editor's eyes on this issue. Jakob.scholbach (talk) 09:03, 29 July 2020 (UTC)
- As per the suggestion of Tazerenix and the suggestion above, I have moved the article to "Nonabelian Hodge correspondence". Jakob.scholbach (talk) 08:57, 30 July 2020 (UTC)