By J. W.P. Hirschfeld,G. Korchmáros,F. Torres

This publication offers an available and self-contained advent to the idea of algebraic curves over a finite box, a subject matter that has been of primary value to arithmetic for a few years and that has crucial functions in parts akin to finite geometry, quantity conception, error-correcting codes, and cryptology. in contrast to different books, this one emphasizes the algebraic geometry instead of the functionality box method of algebraic curves.

The authors start by way of constructing the overall idea of curves over any box, highlighting peculiarities taking place for confident attribute and requiring of the reader basically uncomplicated wisdom of algebra and geometry. The exact homes curve over a finite box could have are then mentioned. The geometrical conception of linear sequence is used to discover estimates for the variety of rational issues on a curve, following the speculation of Stöhr and Voloch. The technique of Hasse and Weil through zeta capabilities is defined, after which consciousness turns to extra complicated effects: a cutting-edge advent to maximal curves over finite fields is equipped; a complete account is given of the automorphism crew of a curve; and a few functions to coding conception and finite geometry are defined. The ebook contains many examples and workouts. it's an necessary source for researchers and the appropriate textbook for graduate students.