By J. W.P. Hirschfeld,G. Korchmáros,F. Torres
This booklet presents an available and self-contained creation to the speculation of algebraic curves over a finite box, an issue that has been of basic significance to arithmetic for a few years and that has crucial functions in components corresponding to finite geometry, quantity concept, 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 commence via constructing the overall thought of curves over any box, highlighting peculiarities happening for confident attribute and requiring of the reader merely simple wisdom of algebra and geometry. The precise 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 idea of Stöhr and Voloch. The technique of Hasse and Weil through zeta features is defined, after which cognizance 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 team of a curve; and a few purposes to coding thought and finite geometry are defined. The ebook contains many examples and routines. it's an essential source for researchers and the right textbook for graduate students.
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Extra resources 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