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Jun 15, 2010 at 21:39 vote accept Mark Rinehold
Jun 15, 2010 at 18:11 comment added Boyarsky @Felipe, I will be amazed if someone who knows algebraic geometry from the given sources can deal with it over a field not algebraically closed. Also, Reid's book avoids Riemann-Roch, so genus will be tough to use algebraically, let alone over finite fields. There's always plane curves, but undergraduate research in these areas seems a dubious idea. Perhaps another crucial word is missing: elementary number theory or algebraic number theory?
Jun 15, 2010 at 17:46 history answered Felipe Voloch CC BY-SA 2.5