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Let f:X -> Y be a morphism of schemes over a field k. Can one check that f is formally smooth 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.

Let $f:X\rightarrow Y$ be a morphism of schemes over a field $k$. Can one check that $f$ is formally smooth using only Artin rings of the form $k^{\prime}\left[t\right]/t^{n}$, where $k^{\prime}$ is also a field?

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

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

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

Let f:X -> Y be a morphism of schemes over a field k. Can one check that f is formally smooth 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.

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

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

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

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