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We know that the product of two spectral topological spaces is spectral.

  • If $X$ is the underlying space of the scheme $\mathrm{Spec}\,\mathbb{Z}[x]$, what is a simple example of an affine scheme whose underlying space is $X\times X$?
  • If $X$ is the underlying space of the scheme $\mathrm{Spec}\,\mathbb{C}[x]$, what is a simple example of an affine scheme whose underlying space is $X\times X$?
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  • $\begingroup$ btw, your link shows you could associate a scheme in principle, can you associate a scheme functorially? Kind of modified product of schemes? $\endgroup$
    – user138661
    Commented May 6, 2019 at 13:26
  • $\begingroup$ @schematic_boi Meta discussion that may be relevant: meta.mathoverflow.net/questions/4200/flood-of-new-users $\endgroup$
    – Yemon Choi
    Commented May 6, 2019 at 22:56

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