Let $Y$ be a reduced noetherian $1$-dimensional scheme such that the normalization morphism $f:X \longrightarrow Y$ is finite. Let $g:Y\longrightarrow Z$ be a finite flat morphism, where $Z$ is a connected (1-dimensional) Dedekind scheme.

Suppose that the morphism $g\circ f$ from $X$ to $Z$ is etale.

**Question.** Is the morphism $g:Y\longrightarrow Z$ etale?

**Remark.** The hypothesis on the dimension is not necessary probably.

**Remark.** One may assume $Y$ to be integral.

**Remark.** To assure that $f$ is finite one may suppose that $Y$ is excellent.

Interesting cases one may consider are $Z\subset \mathrm{Spec} \mathbf{Z}$ or $Z\subset \mathbf{P}^1_k$ non-empty open.