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Jun 3, 2010 at 23:41 answer added Georges Elencwajg timeline score: 4
Jun 3, 2010 at 20:20 comment added Paul Siegel You will have to wait for an algebraic geometer to get a precise answer (perhaps you already have one below), but there is good motivation for taking differential forms as more fundamental in differential topology. Specifically, differential forms are easily organized into a cohomology theory while vector fields are not. I suspect, but cannot verify from experience, that one's interest in differential forms on a scheme also stems from their relation to cohomology.
Jun 3, 2010 at 20:13 answer added Heinrich Hartmann timeline score: 3
Jun 3, 2010 at 19:27 answer added Donu Arapura timeline score: 5
Jun 3, 2010 at 18:34 history asked user2330 CC BY-SA 2.5