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Jan 19, 2011 at 16:22 comment added Georges Elencwajg Dear Matt, you are perfectly right, of course. What I meant was that algebraic group theorists were the ones who wrote introductory books from this functorial point of view ( another nice example being Waterhouse's Introduction to affine group schemes). I am not foolish enough to pontificate about which algebraic geometers do what in their research papers...
Jan 19, 2011 at 15:55 comment added Emerton Dear Georges and Brian, Arithmetic geometers also use this view-point a lot. E.g. if memory serves, my first serious exposure to it was when reading Deligne--Rapoport and Katz on moduli of elliptic curves, and Mazur's Eisenstein Ideal paper (which does involve a lot of computations with group schemes (!) --- but finite flat commutative ones). Regards, Matthew
Jan 19, 2011 at 13:29 comment added Brian Thanks! I will look into this. You do a very good job at promoting the book :-).
Jan 19, 2011 at 12:53 history answered Georges Elencwajg CC BY-SA 2.5