Wednesday, March 16, 2011

notes for next (??and/or last ...) discussion with todd

??[ag theory of [quasicoherent sheaves over [a pre-stack (??or something) on site category of affine schemes]]] defined by kan extension ... "globalization of concept of module of commutative ring" ... ???something about adjunction to "spectrum of an ag theory" and so forth ... ???something about "galois connection" and "fixed point" here ... ???....

??todd suggests relationship to lawvere's ideas about "isbell conjugation" and so forth ...

???so how do toposes get involved here??? ..... and so forth .... ???.... ???something about ... ???toposes vs stacks (or something...) here .... ???something about ... ??the way at the moment "quasicoherent" seems to make some sense in "stack" context but less so in "topos" context .... ???or something ???? .... and so forth .... ???....

??really seeming now like ... ??in fact "you don't have to worry about quasicoherence in the topos context" ...??or something ... ???which perhaps we more or less already realized before .... ???...

??something about "toric case" and so forth ... ???

??something about "fan as maximal atlas" and so forth ... ???

??something about "toric quasicoherent sheaf" ... ??as ordinary quasicoherent sheaf equipped with kind of extra structure, defined in terms of extra toric structure on variety .... ???and so forth ... ???...

??todd asks about "quasicoherentization" (or something ....) and relationship to something in toric case ... ??concerning "accidental topos" ... ??? and so forth ... ???....

??something about ... toric mother topos ... and so forth .... ???....

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