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Record Nr. |
UNINA9910786795203321 |
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Autore |
Hirschfeld J. W. P (James William Peter), <1940-> |
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Titolo |
Algebraic curves over a finite field / / J. W. P. Hirschfeld, G. Korchmaros, F. Torres |
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Pubbl/distr/stampa |
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Princeton, New Jersey : , : Princeton University Press, , 2008 |
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©2008 |
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ISBN |
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Edizione |
[Course Book] |
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Descrizione fisica |
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1 online resource (717 p.) |
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Collana |
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Princeton Series in Applied Mathematics |
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Classificazione |
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Disciplina |
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Soggetti |
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Curves, Algebraic |
Finite fields (Algebra) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Front matter -- Contents -- Preface -- PART 1. General theory of curves -- Chapter One. Fundamental ideas -- Chapter Two. Elimination theory -- Chapter Three. Singular points and intersections -- Chapter Four. Branches and parametrisation -- Chapter Five. The function field of a curve -- Chapter Six. Linear series and the Riemann-Roch Theorem -- Chapter Seven. Algebraic curves in higher-dimensional spaces -- PART 2. Curves over a finite field -- Chapter Eight. Rational points and places over a finite field -- Chapter Nine. Zeta functions and curves with many rational points -- PART 3. Further developments -- Chapter Ten. Maximal and optimal curves -- Chapter Eleven. Automorphisms of an algebraic curve -- Chapter Twelve. Some families of algebraic curves -- Chapter Thirteen. Applications: codes and arcs -- Appendix A. Background on field theory and group theory -- Appendix B. Notation -- Bibliography -- Index |
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Sommario/riassunto |
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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-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 |
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