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Jan 20, 2012 at 16:31 comment added Donu Arapura This is certainly my experience. I suspect that if you did an MRI of working algebraic geometer, you'd see a lot of activity in the visual cortex. (Not that I'm volunteering.)
Jan 20, 2012 at 10:10 comment added quim Since the OP asks specifically about schemes and number theory, let me add that we also see nice pictures of nonreduced things (as thickenings of reduced things), of families (whose base may be "discrete", as Spec Z), maps (coverings come to mind) and probably more.
Jan 20, 2012 at 8:11 history answered S. Carnahan CC BY-SA 3.0