In French, one refers to a certain 'morphisme net'. I am looking for the English translation of this.
EDIT: The term appears here on p.22 Lemme 2.7.2. Unfortunately I have not been able to find the French definition either.
Thanks!
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$\begingroup$ Where did you encounter the term? It would help us to know what contexts it is used in. $\endgroup$– Milo BrandtCommented Aug 18, 2015 at 15:54
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$\begingroup$ It would be good if you could give the definition (in translation). $\endgroup$– Zhen LinCommented Aug 18, 2015 at 15:55
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$\begingroup$ A guess: Perhaps they mean a net of morphisms in some category? $\endgroup$– Alex G.Commented Aug 18, 2015 at 15:57
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1$\begingroup$ I've added a link to the paper I am looking at; I don't think it is a net of morphisms. $\endgroup$– Tian AnCommented Aug 18, 2015 at 16:02
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$\begingroup$ It reminds me of exact sequences. $\endgroup$– pjs36Commented Aug 18, 2015 at 16:09
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1 Answer
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In [SGA 1, Exposé I, Dfn 3.2], "morphisme net" or "morphisme non ramifié" refers to a morphism $X \to Y$ of finite type such that the relative diagonal $X \to X \times_Y X$ is an open immersion. This is called an unramified morphism in English, although sometimes one generalises to morphisms locally of finite type.
answered Aug 18, 2015 at 16:09