Talk:Cohomology

message: It seems a bit silly that this page is basically only about singular cohomology of spaces. Of course something like l-adic cohomology should also be added, but also related notions like group cohomology, etc MeowMathematics (talk) 16:40, 23 January 2024 (UTC)
thread_title:  Other appearances of cohomology 

message: 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)
thread_title:  Question 

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

text: 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)
thread_title:  Deligne cohomology 

message: Is there a definition of cochain on wikipedia?. Clicking on "cocycles" in this article goes to a disambiguation with a link to cochain which is redirected to this cohomology page (unsigned)
:Look at chain complex.  Perhaps cochain should redirect there instead. Silly rabbit 19:12, 22 June 2007 (UTC)
thread_title: Definition of cochain?

message: The history section is very interesting. So, what happened after 1948? Randomblue (talk) 12:40, 14 September 2008 (UTC)
thread_title:  History section 

message: As a graduate student in algebraic topology, I'd say that "generalized cohomology theory" is the standard term for cohomology theories that don't satisfy the dimension axiom.  "Extraordinary cohomology theory" is an outdated term.  (Note for example, the book "Generalized cohomology" by Kono and Tamaki from 2006).  I'm making the relevant changes. 75.3.116.141 (talk) 00:35, 10 March 2010 (UTC)
thread_title:  Terminology 

message: this statement is incorrect. for generalized cohomology theory uniqueness follows from the AHSS, and there is more information then purely the coefficient, like k invariants.  If what is written was correct, generalized cohomology theories would have been as easy to compute as ordinary cohomology, which is not the case.
— Preceding unsigned comment added by 141.223.215.24 (talk) 03:13, 27 June 2012 (UTC)
thread_title:  "cohomology is determined by its values on a point" 

message: What does any of that mean in English?66.19.240.5 (talk) 17:18, 26 February 2014 (UTC)
thread_title:  Translation 

message: "Singular cohomology", "Betti cohomology", and "generalized homology theory" redirect here. BTotaro (talk) 21:26, 6 April 2016 (UTC)
thread_title: Links

message: Substituted at 01:53, 5 May 2016 (UTC)
thread_title: Assessment comment

message: I plan to revert the page to the version by D.Lazard. After that, a section "Analogy" was added with an explanation of cohomology as the "footsteps" left by a topological space. A vivid phrase can be a good thing, but I don't think this particular analogy helps anybody; it's too far from what cohomology is about (as opposed to any other distinguishing feature of anything). In any case, a whole section about this analogy is too much. BTotaro (talk) 22:39, 17 April 2017 (UTC)
thread_title: Edit reverted

message: This page should discuss the cohomology of more refined objects such as varieties. This should mention tools such as derived functors, hodge structures, etale cohomology, etc. and some of the important theorems relating these cohomology theories with singular cohomology. In addition, there should be a discussion about the cohomology of more general spaces such as stacks. All of this should include explicit examples with explanations for their computation.
Some references include:
https://www.math.ubc.ca/~behrend/CohSta-1.pdf
http://digitalassets.lib.berkeley.edu/etd/ucb/text/Sun_berkeley_0028E_10484.pdf
https://math.stackexchange.com/questions/1020065/compute-the-cohomology-of-projective-schemes?rq=1  — Preceding unsigned comment added by 128.138.65.175 (talk) 21:03, 7 September 2017 (UTC)
thread_title:  Discuss Cohomology of Varieties, Stacks, etc.