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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