Title: Algebraic curves over a finite field /
Authors: Hirschfeld, J. W. P. 1940-; Korchmáros, G.; Torres, F.; Torres, F.
Publisher: Princeton University Press,
Year: 2008
Subjects: Curves, Algebraic.; Finite fields (Algebra); Algebraic fields.; Functions, Zeta.; MATHEMATICS Algebra Abstract; MATHEMATICS Algebra Abstract.; MATHEMATICS Geometry General.
Abstract: This title provides a self-contained introduction to the theory of algebraic curves over a finite field, whose origins can be traced back to the works of Gauss and Galois on algebraic equations in two variables with coefficients modulo a prime number.
Contents: Fundamental ideas -- Elimination theory -- Singular points and intersections -- Branches and parametrisation -- The function field of a curve -- Linear series and the Riemann-Roch theorem -- Algebraic curves in higher-dimensional spaces -- Rational points and places over a finite field -- Zeta functions and curves with many rational points -- Maximal and optimal curves -- Automorphisms of an algebraic curve -- Some families of algebraic curves -- Applications: codes and arcs.