Irrational components of the Hilbert scheme of points

We construct irrational irreducible components of the Hilbert scheme of points of affine n-dimensional space, for n at least 12. We start with irrational components of the Hilbert scheme of curves in P³ and use methods developed by Jelisiejew to relate these to irreducible components of the Hilbert schemes of points of Aⁿ. The result solves Problem XX of J. Jelisiejew, Open problems in deformations of Artinian algebras, Hilbert schemes and around, arXiv: 2307. 08777, 2023.