In this question on MO, it can be read:
Indeed $\mathrm{Gal}(\mathbb{Q}^{ab})=\pi_1^c(\mathrm{Spec}(\mathbb{Q}))$ ($c$ stands for the commutator subgroup).
I'm trying to understand what this means. But I don't see what is $\mathrm{Spec}(\mathbb{Q})$. The spectrum of a field (defined as the space of prime ideals) is just a singleton, so I don't think $\mathrm{Spec}(\mathbb{Q})$ should be understood in that sense. But I don't know what it means, then.
As Alex Youcis pointed out below, I was right about $\mathrm{Spec}(\mathbb{Q})$. But then I don't understand what $\pi_1$ means in that context.
Thank you for your comments.