In these notes, https://math.mit.edu/juvitop/old/notes/stackstalk.pdf on pg.4 the author says: "The whole point here is given a ring $R$ we can construct a stack, called ${\rm Spec}(R) = G_R$...", but unfortunately he does not define it. While browsing on google, I wasn't able to find out an explicit definition. Can you please help me out with the definition of a stack associated to a ring $R$? References regarding this construction are welcomed too.
2026-03-28 08:49:12.1774687752
Definition of stack associated to a ring.
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For any ring R, consider the functor of points Hom(-,Spec(R)) of the corresponding affine scheme Spec(R). It gives a sheaf of sets in reasonable topologies, like Zariski, fpqc, etc. Now considering a set as a groupoid, we get that Hom(-,Spec(R)) is a sheaf of groupoids and by definition a stack.