On algebraic curves over a finite field with many rational points (Q1590242)

The paper deals with bounds for the number of rational points over finite fields for algebraic curves having a plane model (possibly with singularities) defined over the finite field in question. It is a natural continuation of the work of \textit{J. W. P. Hirschfeld} and \textit{G. Korchmáros} [Bull. Belg. Math. Soc.-Simon Stevin 5, 313-340 (1998; Zbl 0924.11053)]. The main ingredient here is Stöhr-Voloch theory of Frobenius orders of a morphism [\textit{K.-O. Stöhr} and \textit{J. F. Voloch}, Proc. Lond. Math. Soc. (3) 52, 1-19 (1986; Zbl 0593.14020)].