Algebraic curves over a finite field / / J. W. P. Hirschfeld, G. Korchmaros, F. Torres |
Autore | Hirschfeld J. W. P (James William Peter), <1940-> |
Edizione | [Course Book] |
Pubbl/distr/stampa | Princeton, New Jersey : , : Princeton University Press, , 2008 |
Descrizione fisica | 1 online resource (717 p.) |
Disciplina | 516.352 |
Collana | Princeton Series in Applied Mathematics |
Soggetto topico |
Curves, Algebraic
Finite fields (Algebra) |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4008-4741-9 |
Classificazione | SK 240 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 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 |
Record Nr. | UNINA-9910465028903321 |
Hirschfeld J. W. P (James William Peter), <1940-> | ||
Princeton, New Jersey : , : Princeton University Press, , 2008 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebraic curves over a finite field / / J. W. P. Hirschfeld, G. Korchmaros, F. Torres |
Autore | Hirschfeld J. W. P (James William Peter), <1940-> |
Edizione | [Course Book] |
Pubbl/distr/stampa | Princeton, New Jersey : , : Princeton University Press, , 2008 |
Descrizione fisica | 1 online resource (717 p.) |
Disciplina | 516.352 |
Collana | Princeton Series in Applied Mathematics |
Soggetto topico |
Curves, Algebraic
Finite fields (Algebra) |
Soggetto non controllato |
Abelian group
Abelian variety Affine plane Affine space Affine variety Algebraic closure Algebraic curve Algebraic equation Algebraic extension Algebraic function Algebraic geometry Algebraic integer Algebraic number field Algebraic number theory Algebraic number Algebraic variety Algebraically closed field Applied mathematics Automorphism Birational invariant Characteristic exponent Classification theorem Clifford's theorem Combinatorics Complex number Computation Cyclic group Cyclotomic polynomial Degeneracy (mathematics) Degenerate conic Divisor (algebraic geometry) Divisor Dual curve Dual space Elliptic curve Equation Fermat curve Finite field Finite geometry Finite group Formal power series Function (mathematics) Function field Fundamental theorem Galois extension Galois theory Gauss map General position Generic point Geometry Homogeneous polynomial Hurwitz's theorem Hyperelliptic curve Hyperplane Identity matrix Inequality (mathematics) Intersection number (graph theory) Intersection number J-invariant Line at infinity Linear algebra Linear map Mathematical induction Mathematics Menelaus' theorem Modular curve Natural number Number theory Parity (mathematics) Permutation group Plane curve Point at infinity Polar curve Polygon Polynomial Power series Prime number Projective plane Projective space Quadratic transformation Quadric Resolution of singularities Riemann hypothesis Scalar multiplication Scientific notation Separable extension Separable polynomial Sign (mathematics) Singular point of a curve Special case Subgroup Sylow theorems System of linear equations Tangent Theorem Transcendence degree Upper and lower bounds Valuation ring Variable (mathematics) Vector space |
ISBN | 1-4008-4741-9 |
Classificazione | SK 240 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 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 |
Record Nr. | UNINA-9910786795203321 |
Hirschfeld J. W. P (James William Peter), <1940-> | ||
Princeton, New Jersey : , : Princeton University Press, , 2008 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Algebraic curves over a finite field / / J. W. P. Hirschfeld, G. Korchmaros, F. Torres |
Autore | Hirschfeld J. W. P (James William Peter), <1940-> |
Edizione | [Course Book] |
Pubbl/distr/stampa | Princeton, New Jersey : , : Princeton University Press, , 2008 |
Descrizione fisica | 1 online resource (717 p.) |
Disciplina | 516.352 |
Collana | Princeton Series in Applied Mathematics |
Soggetto topico |
Curves, Algebraic
Finite fields (Algebra) |
Soggetto non controllato |
Abelian group
Abelian variety Affine plane Affine space Affine variety Algebraic closure Algebraic curve Algebraic equation Algebraic extension Algebraic function Algebraic geometry Algebraic integer Algebraic number field Algebraic number theory Algebraic number Algebraic variety Algebraically closed field Applied mathematics Automorphism Birational invariant Characteristic exponent Classification theorem Clifford's theorem Combinatorics Complex number Computation Cyclic group Cyclotomic polynomial Degeneracy (mathematics) Degenerate conic Divisor (algebraic geometry) Divisor Dual curve Dual space Elliptic curve Equation Fermat curve Finite field Finite geometry Finite group Formal power series Function (mathematics) Function field Fundamental theorem Galois extension Galois theory Gauss map General position Generic point Geometry Homogeneous polynomial Hurwitz's theorem Hyperelliptic curve Hyperplane Identity matrix Inequality (mathematics) Intersection number (graph theory) Intersection number J-invariant Line at infinity Linear algebra Linear map Mathematical induction Mathematics Menelaus' theorem Modular curve Natural number Number theory Parity (mathematics) Permutation group Plane curve Point at infinity Polar curve Polygon Polynomial Power series Prime number Projective plane Projective space Quadratic transformation Quadric Resolution of singularities Riemann hypothesis Scalar multiplication Scientific notation Separable extension Separable polynomial Sign (mathematics) Singular point of a curve Special case Subgroup Sylow theorems System of linear equations Tangent Theorem Transcendence degree Upper and lower bounds Valuation ring Variable (mathematics) Vector space |
ISBN | 1-4008-4741-9 |
Classificazione | SK 240 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 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 |
Record Nr. | UNINA-9910812510203321 |
Hirschfeld J. W. P (James William Peter), <1940-> | ||
Princeton, New Jersey : , : Princeton University Press, , 2008 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Applications of curves over finite fields : 1997 AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves over Finite Fields, July 27-31, 1997, University of Washington, Seattle / / Michael D. Fried, editor |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematics Society, , [1999] |
Descrizione fisica | 1 online resource (254 p.) |
Disciplina | 512/.74 |
Collana | Contemporary mathematics |
Soggetto topico |
Finite fields (Algebra)
Curves, Algebraic |
Soggetto genere / forma | Electronic books. |
ISBN | 0-8218-7835-2 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Applications of curves over finite fields""; ""1. Beyond Weil bounds; curves with many rational points""; ""Curve sequences with asymptotically many rational points""; ""Shimura curves over finite fields and their rational points""; ""Distribution of minimal ideals in imaginary quadratic function fields""; ""Division points of Drinfeld modules and special values of Weil L-functions""; ""Constructing curves over finite fields with many points by solving linear equations""; ""On maximal curves having classical Weierstrass gaps""
""2. Monodromy groups of characteristic p covers""""Twice more nice equations for nice groups""; ""Linearized algebra and finite groups of Lie type: I: Linear and symplectic groups""; ""Regular realization of Abelian groups with controlled ramification""; ""On reduction of covers of arithmetic surfaces""; ""Function field sieve method for discrete logarithms over finite fields""; ""3. Zeta functions and trace formulas""; ""A quick introduction to Dwork's conjecture""; ""On the degree of the zeta function of a complete intersection""; ""The modular points of a genus 2 quotient of X0 (67)"" ""Function fields: Arithmetic and applications""""Spanning trees in subgraphs of lattices""; ""Average rank for elliptic curves and a conjecture of Nagao"" |
Record Nr. | UNINA-9910480261003321 |
Providence, Rhode Island : , : American Mathematics Society, , [1999] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Applications of curves over finite fields : 1997 AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves over Finite Fields, July 27-31, 1997, University of Washington, Seattle / / Michael D. Fried, editor |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematics Society, , [1999] |
Descrizione fisica | 1 online resource (254 p.) |
Disciplina | 512/.74 |
Collana | Contemporary mathematics |
Soggetto topico |
Finite fields (Algebra)
Curves, Algebraic |
ISBN | 0-8218-7835-2 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Applications of curves over finite fields""; ""1. Beyond Weil bounds; curves with many rational points""; ""Curve sequences with asymptotically many rational points""; ""Shimura curves over finite fields and their rational points""; ""Distribution of minimal ideals in imaginary quadratic function fields""; ""Division points of Drinfeld modules and special values of Weil L-functions""; ""Constructing curves over finite fields with many points by solving linear equations""; ""On maximal curves having classical Weierstrass gaps""
""2. Monodromy groups of characteristic p covers""""Twice more nice equations for nice groups""; ""Linearized algebra and finite groups of Lie type: I: Linear and symplectic groups""; ""Regular realization of Abelian groups with controlled ramification""; ""On reduction of covers of arithmetic surfaces""; ""Function field sieve method for discrete logarithms over finite fields""; ""3. Zeta functions and trace formulas""; ""A quick introduction to Dwork's conjecture""; ""On the degree of the zeta function of a complete intersection""; ""The modular points of a genus 2 quotient of X0 (67)"" ""Function fields: Arithmetic and applications""""Spanning trees in subgraphs of lattices""; ""Average rank for elliptic curves and a conjecture of Nagao"" |
Record Nr. | UNINA-9910788652203321 |
Providence, Rhode Island : , : American Mathematics Society, , [1999] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Applications of curves over finite fields : 1997 AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves over Finite Fields, July 27-31, 1997, University of Washington, Seattle / / Michael D. Fried, editor |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematics Society, , [1999] |
Descrizione fisica | 1 online resource (254 p.) |
Disciplina | 512/.74 |
Collana | Contemporary mathematics |
Soggetto topico |
Finite fields (Algebra)
Curves, Algebraic |
ISBN | 0-8218-7835-2 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""Applications of curves over finite fields""; ""1. Beyond Weil bounds; curves with many rational points""; ""Curve sequences with asymptotically many rational points""; ""Shimura curves over finite fields and their rational points""; ""Distribution of minimal ideals in imaginary quadratic function fields""; ""Division points of Drinfeld modules and special values of Weil L-functions""; ""Constructing curves over finite fields with many points by solving linear equations""; ""On maximal curves having classical Weierstrass gaps""
""2. Monodromy groups of characteristic p covers""""Twice more nice equations for nice groups""; ""Linearized algebra and finite groups of Lie type: I: Linear and symplectic groups""; ""Regular realization of Abelian groups with controlled ramification""; ""On reduction of covers of arithmetic surfaces""; ""Function field sieve method for discrete logarithms over finite fields""; ""3. Zeta functions and trace formulas""; ""A quick introduction to Dwork's conjecture""; ""On the degree of the zeta function of a complete intersection""; ""The modular points of a genus 2 quotient of X0 (67)"" ""Function fields: Arithmetic and applications""""Spanning trees in subgraphs of lattices""; ""Average rank for elliptic curves and a conjecture of Nagao"" |
Record Nr. | UNINA-9910828537803321 |
Providence, Rhode Island : , : American Mathematics Society, , [1999] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Arithmetic of diagonal hypersurfaces over finite fields / Fernando Q. Gouvea, Noriko Yui |
Autore | Gouvea, Fernando Quadros |
Pubbl/distr/stampa | Cambridge ; New York : Cambridge University Press, 1995 |
Descrizione fisica | xi, 169 p. : ill. ; 23 cm |
Disciplina | 511.7 |
Altri autori (Persone) | Yui, Norikoauthor |
Collana | London Mathematical Society lecture note series, 0076-0552 ; 209 |
Soggetto topico |
Finite fields (Algebra)
Hypersurfaces |
ISBN | 0521498341 |
Classificazione |
AMS 11G25
AMS 14F20 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Record Nr. | UNISALENTO-991000697359707536 |
Gouvea, Fernando Quadros | ||
Cambridge ; New York : Cambridge University Press, 1995 | ||
Materiale a stampa | ||
Lo trovi qui: Univ. del Salento | ||
|
Arithmetic of finite fields : 9th International Workshop, WAIFI 2022, Chengdu, China, August 29-September 2, 2022, revised selected papers / / edited by Sihem Mesnager, Zhengchun Zhou |
Edizione | [1st ed. 2023.] |
Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2023] |
Descrizione fisica | 1 online resource (353 pages) |
Disciplina | 910.5 |
Collana | Lecture Notes in Computer Science |
Soggetto topico | Finite fields (Algebra) |
ISBN | 3-031-22944-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Structures in Finite Fields -- On a conjecture on irreducible polynomials over finite fields with restricted coefficients -- On two applications of polynomials xk – cx – d over finite fields and more -- Efficient Finite Field Arithmetic -- Polynomial Constructions of Chudnovsky-Type Algorithms for Multiplication in Finite Fields with Linear Bilinear Complexity -- Reduction-free Multiplication for Finite Fields and Polynomial Rings -- Finite Field Arithmetic in Large Characteristic for Classical and Post-Quantum Cryptography -- Fast enumeration of superspecial hyperelliptic curves of genus 4 with automorphism group V4 -- Coding theory -- Two Classes of Constacyclic Codes with Variable Parameters -- Near MDS Codes with Dimension 4 and Their Application in Locally Recoverable Codes -- Optimal possibly nonlinear 3-PIR codes of small size -- PIR codes from combinatorial structures -- The Projective General Linear Group PGL(2, 5m) and Linear Codes of Length 5m + 1 -- Private Information Retrieval Schemes Using Cyclic Codes -- Two Classes of Optimal Few-Weight Codes over Fq + uFq -- Explicit Non-Malleable Codes from Bipartite Graphs -- Cryptography -- Algebraic Relation of Three MinRank Algebraic Modelings -- Decomposition of Dillon's APN permutation with efficient hardware implementation -- New Versions of Miller-loop Secured against Side-Channel Attacks -- A Class of Power Mappings with Low Boomerang Uniformity -- New Classes of Bent Functions via the Switching Method -- Sequences -- Correlation measure of binary sequence families with trace representation -- Linear complexity of generalized cyclotomic sequences with period pnqm -- On the 2-adic complexity of cyclotomic binary sequences with period p2 and 2p2. |
Record Nr. | UNISA-996508672203316 |
Cham, Switzerland : , : Springer, , [2023] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. di Salerno | ||
|
Arithmetic of finite fields : 9th International Workshop, WAIFI 2022, Chengdu, China, August 29-September 2, 2022, revised selected papers / / edited by Sihem Mesnager, Zhengchun Zhou |
Edizione | [1st ed. 2023.] |
Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2023] |
Descrizione fisica | 1 online resource (353 pages) |
Disciplina | 910.5 |
Collana | Lecture Notes in Computer Science |
Soggetto topico | Finite fields (Algebra) |
ISBN | 3-031-22944-4 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Structures in Finite Fields -- On a conjecture on irreducible polynomials over finite fields with restricted coefficients -- On two applications of polynomials xk – cx – d over finite fields and more -- Efficient Finite Field Arithmetic -- Polynomial Constructions of Chudnovsky-Type Algorithms for Multiplication in Finite Fields with Linear Bilinear Complexity -- Reduction-free Multiplication for Finite Fields and Polynomial Rings -- Finite Field Arithmetic in Large Characteristic for Classical and Post-Quantum Cryptography -- Fast enumeration of superspecial hyperelliptic curves of genus 4 with automorphism group V4 -- Coding theory -- Two Classes of Constacyclic Codes with Variable Parameters -- Near MDS Codes with Dimension 4 and Their Application in Locally Recoverable Codes -- Optimal possibly nonlinear 3-PIR codes of small size -- PIR codes from combinatorial structures -- The Projective General Linear Group PGL(2, 5m) and Linear Codes of Length 5m + 1 -- Private Information Retrieval Schemes Using Cyclic Codes -- Two Classes of Optimal Few-Weight Codes over Fq + uFq -- Explicit Non-Malleable Codes from Bipartite Graphs -- Cryptography -- Algebraic Relation of Three MinRank Algebraic Modelings -- Decomposition of Dillon's APN permutation with efficient hardware implementation -- New Versions of Miller-loop Secured against Side-Channel Attacks -- A Class of Power Mappings with Low Boomerang Uniformity -- New Classes of Bent Functions via the Switching Method -- Sequences -- Correlation measure of binary sequence families with trace representation -- Linear complexity of generalized cyclotomic sequences with period pnqm -- On the 2-adic complexity of cyclotomic binary sequences with period p2 and 2p2. |
Record Nr. | UNINA-9910644268303321 |
Cham, Switzerland : , : Springer, , [2023] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|
Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 / / George Lusztig |
Autore | Lusztig George |
Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
Descrizione fisica | 1 online resource (408 pages) : illustrations |
Disciplina | 512/.2 |
Collana | Annals of Mathematics Studies |
Soggetto topico |
Finite groups
Finite fields (Algebra) Characters of groups |
Soggetto non controllato |
Addition
Algebra representation Algebraic closure Algebraic group Algebraic variety Algebraically closed field Bijection Borel subgroup Cartan subalgebra Character table Character theory Characteristic function (probability theory) Characteristic polynomial Class function (algebra) Classical group Coefficient Cohomology with compact support Cohomology Combination Complex number Computation Conjugacy class Connected component (graph theory) Coxeter group Cyclic group Cyclotomic polynomial David Kazhdan Dense set Derived category Diagram (category theory) Dimension Direct sum Disjoint sets Disjoint union E6 (mathematics) Eigenvalues and eigenvectors Endomorphism Equivalence class Equivalence relation Existential quantification Explicit formula Explicit formulae (L-function) Fiber bundle Finite field Finite group Fourier transform Green's function Group (mathematics) Group action Group representation Harish-Chandra Hecke algebra Identity element Integer Irreducible representation Isomorphism class Jordan decomposition Line bundle Linear combination Local system Mathematical induction Maximal torus Module (mathematics) Monodromy Morphism Orthonormal basis P-adic number Parametrization Parity (mathematics) Partially ordered set Perverse sheaf Pointwise Polynomial Quantity Rational point Reductive group Ree group Schubert variety Scientific notation Semisimple Lie algebra Sheaf (mathematics) Simple group Simple module Special case Standard basis Subset Subtraction Summation Surjective function Symmetric group Tensor product Theorem Two-dimensional space Unipotent representation Vector bundle Vector space Verma module Weil conjecture Weyl group Zariski topology |
ISBN | 1-4008-8177-3 |
Classificazione | SK 260 |
Formato | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- 1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY -- 2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES XW -- 3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY X̅W -- 4. REPRESENTATIONS OF WEYL GROUPS -- 5. CELLS IN WEYL GROUPS -- 6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM -- 7. SOME EXCEPTIONAL GROUPS -- 8. DECOMPOSITION OF INDUCED REPRESENTATIONS -- 9. CLASSICAL GROUPS -- 10. COMPLETION OF THE PROOF OF THEOREM 4.23 -- 11. EIGENVALUES OF FROBENIUS -- 12. ON THE STRUCTURE OF LEFT CELLS -- 13. RELATIONS WITH CONJUGACY CLASSES -- 14. CONCLUDING REMARKS -- APPENDIX -- REFERENCES -- SUBJECT INDEX -- NOTATION INDEX -- Backmatter |
Record Nr. | UNINA-9910154752803321 |
Lusztig George | ||
Princeton, NJ : , : Princeton University Press, , [2016] | ||
Materiale a stampa | ||
Lo trovi qui: Univ. Federico II | ||
|