# Looking for an undergraduate research problem in algebraic geometry or algebraic number theory

I'm looking for a small research problem an undergraduate would be capable of after taking just an abstract algebra course, introductory algebraic geometry (at level of Miles Reid's book and Ideals, Varieties & Algorithms), and a course in number theory. Is there a website that would have a decent listing, or possibly a book one can recommend that may have small open research problems?

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Open problems in algebraic geometry accessible to an advanced undergraduate seem scarce enough that I would keep any I thought of as trade secrets. And at this moment I can't think of anything else mathematical I would keep as a trade secret! –  Alexander Woo Jun 15 '10 at 17:03

Anyway, here is a problem: Find the maximum number of points of a curve of genus $g$ over $\mathbb{F}_q$, for some values of $g,q$ for which this number is not known (check for values at http://www.manypoints.org/ )