Let f:X -> Y be a morphism of schemes over a field k. Can one check that f is [formally smooth][1] using only Artin rings of the form k'[t]/t^n, where k' is also a field?

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