Curves of every genus with many points, I: Abelian and toric families

Andrew Kresch, Joseph L. Wetherell, Michael E. Zieve

Let N_q(g) denote the maximal number of F_q-rational points on any curve of genus g over the finite field F_q. Ihara (for square q) and Serre (for general q) proved that limsup_{g-…