Grothendieck's relative point of view

[Graham White <graham@eecs.qmul.ac.uk>]

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



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]