Algebraic functions and projective curves / David M. Goldschmidt

Auteur: Goldschmidt, David M. (1942-) - AuteurType de document: MonographieCollection: Graduate texts in mathematics ; 215Langue: anglaisPays: Etats UnisÉditeur: New York : Springer, cop. 2003Description: 1 vol. (XVI-179 p.) ; 24 cm ISBN: 9780387954325 ; rel. Résumé: This book provides a self-contained exposition of the theory of algebraic curves without requiring any of the prerequisites of modern algebraic geometry. The self-contained treatment makes this important and mathematically central subject accessible to non-specialists. At the same time, specialists in the field may be interested to discover several unusual topics. Among these are Tates theory of residues, higher derivatives and Weierstrass points in characteristic p, the Stöhr--Voloch proof of the Riemann hypothesis, and a treatment of inseparable residue field extensions. Although the exposition is based on the theory of function fields in one variable, the book is unusual in that it also covers projective curves, including singularities and a section on plane curves. (Source : Springer).Bibliographie: Bibliogr. p. 175-176. Index. Sujets MSC: 14H05 Algebraic geometry -- Curves -- Algebraic functions; function fields
11R42 Number theory -- Algebraic number theory: global fields -- Zeta functions and L-functions of number fields
11R58 Number theory -- Algebraic number theory: global fields -- Arithmetic theory of algebraic function fields
14G10 Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture)
14G50 Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Applications to coding theory and cryptography
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Bibliogr. p. 175-176. Index

This book provides a self-contained exposition of the theory of algebraic curves without requiring any of the prerequisites of modern algebraic geometry. The self-contained treatment makes this important and mathematically central subject accessible to non-specialists. At the same time, specialists in the field may be interested to discover several unusual topics. Among these are Tates theory of residues, higher derivatives and Weierstrass points in characteristic p, the Stöhr--Voloch proof of the Riemann hypothesis, and a treatment of inseparable residue field extensions. Although the exposition is based on the theory of function fields in one variable, the book is unusual in that it also covers projective curves, including singularities and a section on plane curves. (Source : Springer)

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