Tuesday, August 2, 2011

?? dimensionality aspect of delocalization poset ??? .....

?? for example, delocalizations of rational functions in 2 variables .... ???? .... ??? analog of "2d (??limiting case??) fan containing all rays" ?? .... ??? ....

??? "glueing together two copies of affine line along generic point of both" .... ????? .......

?? confusion about spaces as objects of toposes, vs ... ?? as objects of opposite category of model category ???? ..... ???? ..... hmmm..... ???? "formal colimits of affine schemes with only the localizations as the glueing arrows" ... ??? ... vs .... ??? tierney (and so forth...) 's stuff about "spectrum ..." ... ?? involving "local morphisms" (=?= conservative morphisms = anti-localizations) between local rings ..... ????? .... ??? idea of localizing a local ring as peculiar ???? ...... ??? "local localization" ... ???

??? maybe not so much peculiar as impossible ??? .... ??? any paradox here ???? ..... ?? localizing an element in the maximal ideal as ... ??? hmm, so _does_ this always cause complete collapse ??? .... ??? _is_ this pretty much same issue we got really confused about once ???? ..... ?? inverting a nilpotent as drastic, but what about non-nilpotent elements of the maximal ideal ????? ......

?? formal colimits of affine schemes with only the anti-localizations as the gluring arrows ????? ..... ???? localness of ring in this context ??? .... ??? vs in some other context ... ????? ....... ?????? .......

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