Talk:Cohomology

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Are the theories at the bottom then not extraordinary cohomology theories? (unsigned)

That's right. The axioms only make sense in the context of a cohomology theory which is a functor from the category of topological spaces (or some appropriate subcategory). The "Other cohomology theories" (at least the ones I recognize) are functors from some other category, like that of groups or rings or schemes or something. Quasicharacter 03:37, 14 July 2005 (UTC)

[edit] Deligne cohomology

What is Deligne cohomology? Is this the cohomology theory developed in his work "theorie de hodge, tome i,ii,iii"? If so, is Deligne cohomology a standard term? I would rather call it complex analytic deRham cohomology or algebraic deRham cohomology. --Benjamin.friedrich 13:12, 27 October 2006 (UTC)

I believe there may be more than one theory of Deligne cohomology. Charles Matthews 21:34, 27 October 2006 (UTC)

Well, I googled for it, and the usual conclusion (for me): Wikipedia will eventually be seen as having brought some sanity into mathematics on the Web, by actually writing down definitions. There is something fashionably called Deligne cohomology, a.k.a. Beilinson-Deligne cohomology, a.k.a. Cheeger-Simons cohomology. What I'm remembering was an explicit but somewhat modified de Rham-type theory. Perhaps I should look up the Beilinson conjectures, where I think this started to be used a while back. Anyway, there is such a thing that is well known and a theory in its own right. Charles Matthews 21:42, 27 October 2006 (UTC)