so let x be a topos, r a commutative ring in x ... ???... and suppose that y is a "topos over x" ... ?? meaning that we have a geometric morphism from y into x ...??that is "algebraic morphism from x to y" ... call it f ... and suppose that we have a ring hom from f(r) to the underlying ring of a local ring r' in y ... ???then (??according to tierney??) we're supposed to get a unique ... ??... ??geometric morphism from y into the "small zariski spectrum topos of r", st / tw ... ??? or something???....

so suppose r is a commutative ring... and y is a topos, and r' is a "local commutative ring" in y, and h is a ring homomorphism from the "internalization of r in y" to r' ... ???then this is supposed to give us (with some essential uniqueness??...) a geometric morphism f from y to the "small zariski spectrum topos of r" ... and ... ????a "morphism of local commutative rings from the pullback under f of the main local commutative ring in the zariski thing to r' ... ??

??well, so let's think about the corresponding algebraic morphism from the small zariski topos to y ... ?? or something ... ??

??an algebraic morphism from the small zariski topos of r to some topos y picks out a local commutative r-algebra with a certain property ??? ...???namely (??though somewhat tautologically?? ??or something???) the property that ....