By J. W.P. Hirschfeld,G. Korchmáros,F. Torres
This ebook offers an available and self-contained advent to the speculation of algebraic curves over a finite box, a subject matter that has been of basic value to arithmetic for a few years and that has crucial functions in parts resembling finite geometry, quantity thought, error-correcting codes, and cryptology. not like different books, this one emphasizes the algebraic geometry instead of the functionality box method of algebraic curves.
The authors commence through constructing the final idea of curves over any box, highlighting peculiarities happening for optimistic attribute and requiring of the reader simply uncomplicated wisdom of algebra and geometry. The detailed homes curve over a finite box could have are then mentioned. The geometrical concept 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 strategy of Hasse and Weil through zeta services is defined, after which realization turns to extra complex effects: a cutting-edge advent to maximal curves over finite fields is equipped; a entire account is given of the automorphism workforce of a curve; and a few purposes to coding conception and finite geometry are defined. The ebook contains many examples and workouts. it truly is an vital source for researchers and definitely the right textbook for graduate students.
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Extra info for Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics)
Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics) by J. W.P. Hirschfeld,G. Korchmáros,F. Torres