Let f:X -> Y be a morphism of schemes over a field k. Can one check that f is [Formally smooth][1] using only infinitesmal extensions of the form k[t]/t^n?

Considering cuspidal curves one can show that you do at least need arbitrarily large n.


  [1]: http://www.math.columbia.edu/~dejong/algebraic_geometry/stacks-git/more-morphisms.pdf