My question relates to the following thread I opened some weeks ago:
A question regarding Grothendieck , topos and (adelic??) points
Specifically, consider this paragraph:
At 1:14:30 and after,
Toen presents the new objects emerging from topos theory in algebraic geometry. He takes the following example: one wants to solve the algebraic equation X=0 He says that in a classical framework, it just gives us the solution 0, so it's a point. Not that interesting. But with the topos point of view, it gives different solutions depending on where we solve the equation: over C it gives a point (as before), but over a finite field Fp it gives a point together with a (kind of) symmetry. (He represents this last object as a point and loop-edge on the point.)
I would like to know whether the second meaning (that of the topos perspective) relates to the idea of singular point, and, if so, in whch way.
Thanks in advance.