Algebraic Curves over a Finite Field /

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This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correctin...

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Detalles Bibliográficos
Autores principales: Hirschfeld, J. W. P. (James William Peter), 1940- (Autor), Torres, F. (Fernando) (Autor), Korchmáros, G. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, New Jersey : Princeton University Press, 2008.
Colección:Book collections on Project MUSE.
Temas:
Algebraische Kurve
Galois-Feld
Finite fields (Algebra)
Curves, Algebraic.
MATHEMATICS > Algebra > Abstract.
MATHEMATICS > Geometry > General.
Corps finis.
Courbes algebriques.
Electronic books.
Acceso en línea:Texto completo

MARC

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100 1 |a Hirschfeld, J. W. P.  |q (James William Peter),  |d 1940-  |e author. 
245 1 0 |a Algebraic Curves over a Finite Field /   |c J.W.P. Hirschfeld, G. Korchmaros, F. Torres. 
264 1 |a Princeton, New Jersey :  |b Princeton University Press,  |c 2008. 
264 3 |a Baltimore, Md. :  |b Project MUSE,   |c 0000 
264 4 |c ©2008. 
300 |a 1 online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 0 |a Princeton Series in Applied Mathematics 
505 0 |a Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bezout's Theorem. 
505 0 |a 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations. 
505 0 |a 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes. 
505 0 |a Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem. 
505 0 |a 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes. 
520 |a This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi. 
546 |a In English. 
588 |a Description based on print version record. 
650 7 |a Algebraische Kurve  |2 gnd 
650 7 |a Galois-Feld  |2 gnd 
650 7 |a Finite fields (Algebra)  |2 fast  |0 (OCoLC)fst00924905 
650 7 |a Curves, Algebraic.  |2 fast  |0 (OCoLC)fst00885451 
650 7 |a MATHEMATICS  |x Algebra  |x Abstract.  |2 bisacsh 
650 7 |a MATHEMATICS  |x Geometry  |x General.  |2 bisacsh 
650 6 |a Corps finis. 
650 6 |a Courbes algebriques. 
650 0 |a Finite fields (Algebra) 
650 0 |a Curves, Algebraic. 
655 7 |a Electronic books.   |2 local 
700 1 |a Torres, F.  |q (Fernando),  |e author. 
700 1 |a Korchmáros, G.,  |e author. 
710 2 |a Project Muse.  |e distributor 
830 0 |a Book collections on Project MUSE. 
856 4 0 |z Texto completo  |u https://projectmuse.uam.elogim.com/book/35385/ 
945 |a Project MUSE - Custom Collection 

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