Re: Grothendieck's relative point of view

["Eduardo J. Dubuc" <edubuc@dm.uba.ar>]

Graham White wrote:
> I'm looking for some history of what seems to be called "Grothendieck's
> relative point of view":

What about "Grothendieck's change of base", so much used in SGA4, and
extensively advocated and used by Joyal and others by considering the
category of Grothendieck topoi over a given Grothendieck topos (not Sets) ?.

Is not this Grothendieck's relative point of view ?

I am just asking.   e.d.


   the idea that what ostensibly seems to be an
> isolated mathematical object may well be better studied by
> systematically looking at families of such objects. Now Grothendieck
> certainly uses it in his proof of, and generalisation of, Riemann-Roch.
> And there are historical essays in various Wikis that say so. But:
> i) how does he come to this idea?
> ii) are there any places where he talks about it and about what it
> means? What generality is it meant to apply in?
> iii) does anybody before him talk about it? (In particular, there is
> some explicit parametrisation involved in Weil's approach to algebraic
> number theory, and the number field/function field analogy: does Weil
> ever talk explicitly about this?)
>
> Thanks
>
> Graham


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