Talk:Étale morphism

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I removed the reference to monic polynomials in the section concening the localization of k[x_1,...,x_n]/<f_1,...,f_n> since (a) I don't know what a monic polynomial in several variables is and (b) I don't believe such a condition is necessary.

RJChapman 18:57, 27 November 2006 (UTC)

Are the five defintions really equivalent without any hypothesis? J. Milne seems to imply in his lecture notes on etale cohomology (available from his website) on page 13 that the definitions involving the morphism to be locally of finite presentation are weaker than the definition flat+unramified.

-- According to Milne's book on etale cohomology, , p.30, for f : X --> Y they are equivalent: flat + unramified (which is by definition locally of finite type) is equivalent to locally of finite presentation and formally etale (i.e. the functor Hom_X(-, Y) does only see the topological structure of -). Jakob.scholbach 21:17, 17 April 2007 (UTC)

[edit] Pronunciation of étale

Could somebody add an IPA pronunciation of the term étale?

Baccala@freesoft.org 08:09, 29 September 2007 (UTC)