Hello,

Is it true that if I have a scheme $X$ which is, say, Noetherian, of finite Krull dimension, and semi-separated (intersection of two open affines is again open affine), then I can find a locally closed embedding of it into a scheme of the same type, which is, in addition, regular?

I ask just of curiosity, or minor desire not to say "quasi-projective" when I want to have enough locally free objects.

Thank you, Sasha