Properties of varieties that can be lifted under etale morphisms

Question

Let $X$,$Y$ be varieties over some field $k$ of char $0$ (not necessarily algebraically closed). Suppose we have an etale morphism $f : Y \to X$.

My question: for what properties P can we say that if $X$ has P, then $Y$ has also P?

For example if $X$ is proper we can say that $Y$ is also proper. References/proofs are welcome.

Answer 1

Obviously every property P of morphisms works which is stable under composition and contains all etale morphisms. For example "smooth".