Infinite-dimensional affine space over Q diagram

Consists of a scheme $X$, satisfying the following properties:

• $X$ not regular, quasi-compact, affine, integral, connected, reduced, all stalks of the structure sheaf are domains, not noetherian, not locally noetherian, irreducible, not excellent, not cohen-macaulay, not finite dimensional
By the theorems, we also have {"X": {"separated": true}}