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Mar 1, 2016 at 1:50 comment added Tim @javier Could you possibly elaborate on why we know that $\mathrm{Spec}\mathbb{Z}$ cannot be of finite type, no matter what our definition of $\mathbb{F}_1$ is? Sorry if this is an overly simple question.
May 4, 2010 at 13:56 comment added javier Nice explanation! Some of the main problems that one faces at this point are, ignoring for a moment the wild jungle of different approaches, that no matter what your definition of $\mathbb{F}_1$ variety is, $\text{Spec}\mathbb{Z}$ cannot be even of finite type, and moreover nobody has yet come with a nice idea of what on earth a "smooth" $\mathbb{F}_1$ variety is.
May 4, 2010 at 13:20 history answered Kevin H. Lin CC BY-SA 2.5