Talk:Étale cohomology

message: Note on the lower case redirect - I thought there was a possible bug, meaning that lower case e-acute wasn't automatically sent to this Étale cohomology page. Well, I encountered a problem with this, yesterday.
Charles Matthews 11:04, 14 Dec 2003 (UTC)

message: Hi,
I'm sorry if the information is in the article, but why is the concept called etale? I think this means spread in French. Thanks. 131.111.216.28 (talk) 23:08, 13 March 2008 (UTC)
replies: text: I think it comes from the fact that an etale map is analogous to a local diffeomorphism, so if you draw a curve X etale over Y, this looks pretty much spread out... Jakob.scholbach (talk) 11:49, 14 March 2008 (UTC)

text: See etale morphism for the terminology. Jakob.scholbach (talk) 11:49, 14 March 2008 (UTC)
thread_title:  why etale? 

message: I'm no expert so I haven't edited the page, but isn't \mathcal{O}_X^\ast more standard for the sheaf of nonzero functions than G_m? My first guess would have been that H^i(X,G_m) meant cohomology with coefficients in a torus.
/dan  —Preceding unsigned comment added by 85.225.79.77 (talk) 09:11, 3 October 2009 (UTC)
thread_title:  question on notation 

message: I found much help in understanding Et.Coh. from the entry, but also had some questions that maybe one who is confident in these matters may consider if they should be addressed/clarified in the article, e.g.:
* Definition of Et(X): I would appreciate if there were a just slightly more explicit/formal definition of objects and arrows - e.g., is this true: the objects are morphisms f:S->X with f,S (and X) in the category of schemes (category of schemes: also Large?) such that f is etale  (perhaps also: is there a (perhaps even full or faithful) functor from the category of schemes to Et(X) ? if yes, would seem helpful to mention)
::Yes, etale morphisms to X means morphisms S -> X that are etale. No functors around such as you mention. It is inside a slice category of all morphisms to X, if you want more detail. Charles Matthews (talk) 14:48, 8 June 2011 (UTC)
replies: text:  Thanks for your replies! -- That (connection to slice cat.) does indeed help me a little -- I just had a little 'semantic uneasiness' with the formulation 'all etale morphisms from a scheme to X' -- it might wrongly convey 'from (just) one specific scheme to X'... but disregard this at will, if it seems clear enough. Summsumm2 (talk) 15:18, 8 June 2011 (UTC)
replies: text: Makes sense by analogy with say singular cohomology: torsion can occur when the coefficients are integers, but not when the coefficients are rational numbers. Charles Matthews (talk) 14:53, 8 June 2011 (UTC)
replies: text:  Yes, that is how I understood it, my confusion was that 'Torsion can occur' right after discussion of the 'rational coefficients' (where torsion doesn't occur) seems misleading, i.e., would it not be better, e.g., to swap these last two paragraphs ? Summsumm2 (talk) 15:18, 8 June 2011 (UTC)

text: The Gm notation is usually the multiplicative group, but it is defined in the section as an actual sheaf (i.e. a functor form of taking invertible elements of (whatever)). Charles Matthews (talk) 14:53, 8 June 2011 (UTC)
replies: text:  I have seen the definition of G_m, just in the lines before, my concern was about the G_{m,K} ... (again, disregard, if this should be clear to the typical reader)Summsumm2 (talk) 15:18, 8 June 2011 (UTC)
thread_title:  from a learner's pov ... 

message: In the article, it is mentioned that the sheaf Q_l is not etale. But it seems to me that it is just the constant sheaf, which is etale. Please help me out with this confusion.  — Preceding unsigned comment added by 77.13.108.173 (talk) 01:19, 11 June 2012 (UTC)
thread_title:  Etale Sheaf 

message: An interesting computation which should be added in detail is https://mathoverflow.net/questions/281359/computing-the-etale-cohomology-of-spheres  — Preceding unsigned comment added by 70.59.17.182 (talk) 01:39, 18 September 2017 (UTC)
thread_title:  Computations