Monday, March 12, 2012

?? various ideas about particular motivations for introducing "up to a particular level" (?? ...) new colimits of affine algebraic varieties .... ??? ....

?? "modifying the original colimits as little as possible so as to get "points over fields (?? ...)" functors to preserve (?? some ?? ...) colimits" .... ???? .... ?? some sort of "atomicness" (??? ...) of field spectrums .... ???? .....

?? achieving toposness ... ?? but then rejecting it .... ?????? ...... ????? .... morphisms vs objects .... ?? "allowing only flat (?? ...) glueing" ??? ..... ???? ....

??? borrowing colimits from ag theories ...... ?????? ......

?? recycling various ideas mentioned here in "higher" cases ... higher versions of non-/affine .... ??? ....

?? (?? "co-" ???)minimal topos completion (?? ...) of _affine scheme_ .... ????? .....

??? ideas (from (?? ...) toric case ?? ...) about .... ??? comparing [theory morphism] concept to morphism concept defined by ... ?? "recycling glueing of objects concept from "absolute" to "relative" case ..... ????? ..... ?? fixed vs variable base .... ???? ..... ??? 2-colimit ??? ..... ???? ...... ..... ?? affine base vs non-affine base ..... ????? ..... ???? ....

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