F-pure Thresholds and F-jumping Exponents in Dimension Two

Using an argument based on an idea of Monsky, we prove the rationality of the F-pure thresholds of curve singularities on a smooth surface defined over a finite field. More generally, we prove in this setting the rationality and discreteness of F-jumping exponents, the smallest positive one of which is the F-pure threshold. We also give a lower bound for F-pure thresholds in the homogeneous case.