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Mar 29, 2016 at 10:08 comment added naf Wofgang Schmidt has considered Stepanov's method in higher dimensions but doesn't get what Deligne does. See, for example, his book "Equations over finite fields. An elementary approach", SLNM, 536.
Mar 29, 2016 at 1:15 comment added Will Sawin My understanding is that elementary methods usually have difficulty taking advantage of smoothness, but that's not a guarantee...
Mar 29, 2016 at 0:39 history asked Vesselin Dimitrov CC BY-SA 3.0