*Formally étale* means that the infinitesimal lifting property is *uniquely* satisfied. If the map is also locally of finite presentation, then it is called *étale*. One of many characterizations (see EGA 4.5.17) of *étale* is flat and unramified. So my question is whether the weaker condition of *formally étale* still implies flatness?



Does formally etale imply flat?
It seems that Anton Geraschenkos answer to a previous question [Is there an example of a formally smooth morphism that is not smooth](https://mathoverflow.net/questions/195/is-there-an-example-of-a-formally-smooth-morphism-which-is-not-smooth) does the trick here as well. His example of a formally smooth map that is not flat is indeed formally etale. So, formally etale does **not** imply flat.


