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A classical introduction to Galois theory [[electronic resource] /] / Stephen C. Newman
| A classical introduction to Galois theory [[electronic resource] /] / Stephen C. Newman |
| Autore | Newman Stephen C. <1952-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2012 |
| Descrizione fisica | 1 online resource (298 p.) |
| Disciplina | 512/.32 |
| Soggetto topico | Galois theory |
| ISBN |
1-280-67898-4
9786613655912 1-118-33684-4 1-118-33681-X 1-118-33667-4 |
| Classificazione | MAT003000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
A CLASSICAL INTRODUCTION TO GALOIS THEORY; CONTENTS; PREFACE; 1 CLASSICAL FORMULAS; 1.1 Quadratic Polynomials; 1.2 Cubic Polynomials; 1.3 Quartic Polynomials; 2 POLYNOMIALS AND FIELD THEORY; 2.1 Divisibility; 2.2 Algebraic Extensions; 2.3 Degree of Extensions; 2.4 Derivatives; 2.5 Primitive Element Theorem; 2.6 Isomorphism Extension Theorem and Splitting Fields; 3 FUNDAMENTAL THEOREM ON SYMMETRIC POLYNOMIALS AND DISCRIMINANTS; 3.1 Fundamental Theorem on Symmetric Polynomials; 3.2 Fundamental Theorem on Symmetric Rational Functions; 3.3 Some Identities Based on Elementary Symmetric Polynomials
3.4 Discriminants3.5 Discriminants and Subfields of the Real Numbers; 4 IRREDUCIBILITY AND FACTORIZATION; 4.1 Irreducibility Over the Rational Numbers; 4.2 Irreducibility and Splitting Fields; 4.3 Factorization and Adjunction; 5 ROOTS OF UNITY AND CYCLOTOMIC POLYNOMIALS; 5.1 Roots of Unity; 5.2 Cyclotomic Polynomials; 6 RADICAL EXTENSIONS AND SOLVABILITY BY RADICALS; 6.1 Basic Results on Radical Extensions; 6.2 Gauss's Theorem on Cyclotomic Polynomials; 6.3 Abel's Theorem on Radical Extensions; 6.4 Polynomials of Prime Degree; 7 GENERAL POLYNOMIALS AND THE BEGINNINGS OF GALOIS THEORY 7.1 General Polynomials7.2 The Beginnings of Galois Theory; 8 CLASSICAL GALOIS THEORY ACCORDING TO GALOIS; 9 MODERN GALOIS THEORY; 9.1 Galois Theory and Finite Extensions; 9.2 Galois Theory and Splitting Fields; 10 CYCLIC EXTENSIONS AND CYCLOTOMIC FIELDS; 10.1 Cyclic Extensions; 10.2 Cyclotomic Fields; 11 GALOIS'S CRITERION FOR SOLVABILITY OF POLYNOMIALS BY RADICALS; 12 POLYNOMIALS OF PRIME DEGREE; 13 PERIODS OF ROOTS OF UNITY; 14 DENESTING RADICALS; 15 CLASSICAL FORMULAS REVISITED; 15.1 General Quadratic Polynomial; 15.2 General Cubic Polynomial; 15.3 General Quartic Polynomial APPENDIX A COSETS AND GROUP ACTIONSAPPENDIX B CYCLIC GROUPS; APPENDIX C SOLVABLE GROUPS; APPENDIX D PERMUTATION GROUPS; APPENDIX E FINITE FIELDS AND NUMBER THEORY; APPENDIX F FURTHER READING; REFERENCES; INDEX |
| Record Nr. | UNINA-9910139550803321 |
Newman Stephen C. <1952->
|
||
| Hoboken, N.J., : Wiley, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A classical introduction to Galois theory / / Stephen C. Newman
| A classical introduction to Galois theory / / Stephen C. Newman |
| Autore | Newman Stephen C. <1952-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2012 |
| Descrizione fisica | 1 online resource (298 p.) |
| Disciplina | 512/.32 |
| Soggetto topico | Galois theory |
| ISBN |
1-280-67898-4
9786613655912 1-118-33684-4 1-118-33681-X 1-118-33667-4 |
| Classificazione | MAT003000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
A CLASSICAL INTRODUCTION TO GALOIS THEORY; CONTENTS; PREFACE; 1 CLASSICAL FORMULAS; 1.1 Quadratic Polynomials; 1.2 Cubic Polynomials; 1.3 Quartic Polynomials; 2 POLYNOMIALS AND FIELD THEORY; 2.1 Divisibility; 2.2 Algebraic Extensions; 2.3 Degree of Extensions; 2.4 Derivatives; 2.5 Primitive Element Theorem; 2.6 Isomorphism Extension Theorem and Splitting Fields; 3 FUNDAMENTAL THEOREM ON SYMMETRIC POLYNOMIALS AND DISCRIMINANTS; 3.1 Fundamental Theorem on Symmetric Polynomials; 3.2 Fundamental Theorem on Symmetric Rational Functions; 3.3 Some Identities Based on Elementary Symmetric Polynomials
3.4 Discriminants3.5 Discriminants and Subfields of the Real Numbers; 4 IRREDUCIBILITY AND FACTORIZATION; 4.1 Irreducibility Over the Rational Numbers; 4.2 Irreducibility and Splitting Fields; 4.3 Factorization and Adjunction; 5 ROOTS OF UNITY AND CYCLOTOMIC POLYNOMIALS; 5.1 Roots of Unity; 5.2 Cyclotomic Polynomials; 6 RADICAL EXTENSIONS AND SOLVABILITY BY RADICALS; 6.1 Basic Results on Radical Extensions; 6.2 Gauss's Theorem on Cyclotomic Polynomials; 6.3 Abel's Theorem on Radical Extensions; 6.4 Polynomials of Prime Degree; 7 GENERAL POLYNOMIALS AND THE BEGINNINGS OF GALOIS THEORY 7.1 General Polynomials7.2 The Beginnings of Galois Theory; 8 CLASSICAL GALOIS THEORY ACCORDING TO GALOIS; 9 MODERN GALOIS THEORY; 9.1 Galois Theory and Finite Extensions; 9.2 Galois Theory and Splitting Fields; 10 CYCLIC EXTENSIONS AND CYCLOTOMIC FIELDS; 10.1 Cyclic Extensions; 10.2 Cyclotomic Fields; 11 GALOIS'S CRITERION FOR SOLVABILITY OF POLYNOMIALS BY RADICALS; 12 POLYNOMIALS OF PRIME DEGREE; 13 PERIODS OF ROOTS OF UNITY; 14 DENESTING RADICALS; 15 CLASSICAL FORMULAS REVISITED; 15.1 General Quadratic Polynomial; 15.2 General Cubic Polynomial; 15.3 General Quartic Polynomial APPENDIX A COSETS AND GROUP ACTIONSAPPENDIX B CYCLIC GROUPS; APPENDIX C SOLVABLE GROUPS; APPENDIX D PERMUTATION GROUPS; APPENDIX E FINITE FIELDS AND NUMBER THEORY; APPENDIX F FURTHER READING; REFERENCES; INDEX |
| Record Nr. | UNISA-996197528903316 |
|
Newman Stephen C. <1952->
|
||
| Hoboken, N.J., : Wiley, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
A classical introduction to Galois theory / / Stephen C. Newman
| A classical introduction to Galois theory / / Stephen C. Newman |
| Autore | Newman Stephen C. <1952-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2012 |
| Descrizione fisica | 1 online resource (298 p.) |
| Disciplina | 512/.32 |
| Soggetto topico | Galois theory |
| ISBN |
1-280-67898-4
9786613655912 1-118-33684-4 1-118-33681-X 1-118-33667-4 |
| Classificazione | MAT003000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
A CLASSICAL INTRODUCTION TO GALOIS THEORY; CONTENTS; PREFACE; 1 CLASSICAL FORMULAS; 1.1 Quadratic Polynomials; 1.2 Cubic Polynomials; 1.3 Quartic Polynomials; 2 POLYNOMIALS AND FIELD THEORY; 2.1 Divisibility; 2.2 Algebraic Extensions; 2.3 Degree of Extensions; 2.4 Derivatives; 2.5 Primitive Element Theorem; 2.6 Isomorphism Extension Theorem and Splitting Fields; 3 FUNDAMENTAL THEOREM ON SYMMETRIC POLYNOMIALS AND DISCRIMINANTS; 3.1 Fundamental Theorem on Symmetric Polynomials; 3.2 Fundamental Theorem on Symmetric Rational Functions; 3.3 Some Identities Based on Elementary Symmetric Polynomials
3.4 Discriminants3.5 Discriminants and Subfields of the Real Numbers; 4 IRREDUCIBILITY AND FACTORIZATION; 4.1 Irreducibility Over the Rational Numbers; 4.2 Irreducibility and Splitting Fields; 4.3 Factorization and Adjunction; 5 ROOTS OF UNITY AND CYCLOTOMIC POLYNOMIALS; 5.1 Roots of Unity; 5.2 Cyclotomic Polynomials; 6 RADICAL EXTENSIONS AND SOLVABILITY BY RADICALS; 6.1 Basic Results on Radical Extensions; 6.2 Gauss's Theorem on Cyclotomic Polynomials; 6.3 Abel's Theorem on Radical Extensions; 6.4 Polynomials of Prime Degree; 7 GENERAL POLYNOMIALS AND THE BEGINNINGS OF GALOIS THEORY 7.1 General Polynomials7.2 The Beginnings of Galois Theory; 8 CLASSICAL GALOIS THEORY ACCORDING TO GALOIS; 9 MODERN GALOIS THEORY; 9.1 Galois Theory and Finite Extensions; 9.2 Galois Theory and Splitting Fields; 10 CYCLIC EXTENSIONS AND CYCLOTOMIC FIELDS; 10.1 Cyclic Extensions; 10.2 Cyclotomic Fields; 11 GALOIS'S CRITERION FOR SOLVABILITY OF POLYNOMIALS BY RADICALS; 12 POLYNOMIALS OF PRIME DEGREE; 13 PERIODS OF ROOTS OF UNITY; 14 DENESTING RADICALS; 15 CLASSICAL FORMULAS REVISITED; 15.1 General Quadratic Polynomial; 15.2 General Cubic Polynomial; 15.3 General Quartic Polynomial APPENDIX A COSETS AND GROUP ACTIONSAPPENDIX B CYCLIC GROUPS; APPENDIX C SOLVABLE GROUPS; APPENDIX D PERMUTATION GROUPS; APPENDIX E FINITE FIELDS AND NUMBER THEORY; APPENDIX F FURTHER READING; REFERENCES; INDEX |
| Record Nr. | UNINA-9910815403803321 |
|
Newman Stephen C. <1952->
|
||
| Hoboken, N.J., : Wiley, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven
| Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2011 |
| Descrizione fisica | 1 online resource (438 p.) |
| Disciplina | 512/.32 |
| Altri autori (Persone) |
EdixhovenB <1962-> (Bas)
CouveignesJean-Marc |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Galois modules (Algebra)
Class field theory |
| Soggetto genere / forma | Electronic books. |
| Soggetto non controllato |
Arakelov invariants
Arakelov theory Fourier coefficients Galois representation Galois representations Green functions Hecke operators Jacobians Langlands program Las Vegas algorithm Lehmer Peter Bruin Ramanujan's tau function Ramanujan's tau-function Ramanujan's tau Riemann surfaces Schoof's algorithm Turing machines algorithms arithmetic geometry arithmetic surfaces bounding heights bounds coefficients complex roots computation computing algorithms computing coefficients cusp forms cuspidal divisor eigenforms finite fields height functions inequality lattices minimal polynomial modular curves modular forms modular representation modular representations modular symbols nonvanishing conjecture p-adic methods plane curves polynomial time algorithm polynomial time algoriths polynomial time polynomials power series probabilistic polynomial time random divisors residual representation square root square-free levels tale cohomology torsion divisors torsion |
| ISBN |
1-283-05180-X
9786613051806 1-4008-3900-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Acknowledgments -- Author information -- Dependencies between the chapters -- Chapter 1. Introduction, main results, context / Edixhoven, Bas -- Chapter 2. Modular curves, modular forms, lattices, Galois representations / Edixhoven, Bas -- Chapter 3. First description of the algorithms / Couveignes, Jean-Marc / Edixhoven, Bas -- Chapter 4. Short introduction to heights and Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 5. Computing complex zeros of polynomials and power series / Couveignes, Jean-Marc -- Chapter 6. Computations with modular forms and Galois representations / Bosman, Johan -- Chapter 7. Polynomials for projective representations of level one forms / Bosman, Johan -- Chapter 8. Description of X1(5l) / Edixhoven, Bas -- Chapter 9. Applying Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 10. An upper bound for Green functions on Riemann surfaces / Merkl, Franz -- Chapter 11. Bounds for Arakelov invariants of modular curves / Edixhoven, B. / de Jong, R. -- Chapter 12. Approximating Vf over the complex numbers / Couveignes, Jean-Marc -- Chapter 13. Computing Vf modulo p / Couveignes, Jean-Marc -- Chapter 14. Computing the residual Galois representations / Edixhoven, Bas -- Chapter 15. Computing coefficients of modular forms / Edixhoven, Bas -- Epilogue -- Bibliography -- Index |
| Record Nr. | UNINA-9910460447203321 |
| Princeton, N.J., : Princeton University Press, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven
| Computational aspects of modular forms and Galois representations [[electronic resource] ] : how one can compute in polynomial time the value of Ramanujan's tau at a prime / / edited by Jean-Marc Couveignes and Bas Edixhoven |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2011 |
| Descrizione fisica | 1 online resource (438 p.) |
| Disciplina | 512/.32 |
| Altri autori (Persone) |
EdixhovenB <1962-> (Bas)
CouveignesJean-Marc |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Galois modules (Algebra)
Class field theory |
| Soggetto non controllato |
Arakelov invariants
Arakelov theory Fourier coefficients Galois representation Galois representations Green functions Hecke operators Jacobians Langlands program Las Vegas algorithm Lehmer Peter Bruin Ramanujan's tau function Ramanujan's tau-function Ramanujan's tau Riemann surfaces Schoof's algorithm Turing machines algorithms arithmetic geometry arithmetic surfaces bounding heights bounds coefficients complex roots computation computing algorithms computing coefficients cusp forms cuspidal divisor eigenforms finite fields height functions inequality lattices minimal polynomial modular curves modular forms modular representation modular representations modular symbols nonvanishing conjecture p-adic methods plane curves polynomial time algorithm polynomial time algoriths polynomial time polynomials power series probabilistic polynomial time random divisors residual representation square root square-free levels tale cohomology torsion divisors torsion |
| ISBN |
1-283-05180-X
9786613051806 1-4008-3900-9 |
| Classificazione | MAT001000MAT012010 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Acknowledgments -- Author information -- Dependencies between the chapters -- Chapter 1. Introduction, main results, context / Edixhoven, Bas -- Chapter 2. Modular curves, modular forms, lattices, Galois representations / Edixhoven, Bas -- Chapter 3. First description of the algorithms / Couveignes, Jean-Marc / Edixhoven, Bas -- Chapter 4. Short introduction to heights and Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 5. Computing complex zeros of polynomials and power series / Couveignes, Jean-Marc -- Chapter 6. Computations with modular forms and Galois representations / Bosman, Johan -- Chapter 7. Polynomials for projective representations of level one forms / Bosman, Johan -- Chapter 8. Description of X1(5l) / Edixhoven, Bas -- Chapter 9. Applying Arakelov theory / Edixhoven, Bas / de Jong, Robin -- Chapter 10. An upper bound for Green functions on Riemann surfaces / Merkl, Franz -- Chapter 11. Bounds for Arakelov invariants of modular curves / Edixhoven, B. / de Jong, R. -- Chapter 12. Approximating Vf over the complex numbers / Couveignes, Jean-Marc -- Chapter 13. Computing Vf modulo p / Couveignes, Jean-Marc -- Chapter 14. Computing the residual Galois representations / Edixhoven, Bas -- Chapter 15. Computing coefficients of modular forms / Edixhoven, Bas -- Epilogue -- Bibliography -- Index |
| Record Nr. | UNINA-9910789850303321 |
| Princeton, N.J., : Princeton University Press, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Elliptic Curves, Hilbert Modular Forms and Galois Deformations / / by Laurent Berger, Gebhard Böckle, Lassina Dembélé, Mladen Dimitrov, Tim Dokchitser, John Voight
| Elliptic Curves, Hilbert Modular Forms and Galois Deformations / / by Laurent Berger, Gebhard Böckle, Lassina Dembélé, Mladen Dimitrov, Tim Dokchitser, John Voight |
| Autore | Berger Laurent |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2013 |
| Descrizione fisica | 1 online resource (XII, 249 p. 11 illus., 2 illus. in color.) |
| Disciplina | 512/.32 |
| Collana | Advanced Courses in Mathematics - CRM Barcelona |
| Soggetto topico |
Number theory
Geometry, Algebraic Algebra Number Theory Algebraic Geometry |
| ISBN | 3-0348-0618-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I: Galois Deformations -- On p-adic Galois Representations -- Deformations of Galois Representations -- Part II: Hilbert Modular Forms -- Arithmetic Aspects of Hilbert Modular Forms and Varieties -- Explicit Methods for Hilbert Modular Forms -- Part III: Elliptic Curves -- Notes on the Parity Conjecture. |
| Record Nr. | UNINA-9910438138203321 |
|
Berger Laurent
|
||
| Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An extension of the Galois theory of Grothendieck / / André Joyal, Myles Tierney
| An extension of the Galois theory of Grothendieck / / André Joyal, Myles Tierney |
| Autore | Joyal André |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1984 |
| Descrizione fisica | 1 online resource (87 p.) |
| Disciplina | 512/.32 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Toposes
Galois theory Theory of descent (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0722-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""Introduction""; ""Chapter I � Sup�lattices""; ""1. Definitions and duality""; ""2. Limits and colimits""; ""3. Free sup�lattices""; ""4. Sub and quotient lattices""; ""5. Tensor products""; ""Chapter II � Rings, modules and descent""; ""1. Rings and modules""; ""2. Tensor product of modules""; ""3. Change of rings""; ""4. Flatness, projectivity, and purity""; ""5. Descent theory for modules""; ""Chapter III � Locales""; ""1. Locales and commutative monoids""; ""2. Limits and colimits""; ""3. The free locale""; ""4. Local operators and quotients""
""5. The splitting locale""""Chapter IV � Spaces""; ""1. Subspaces""; ""2. Points and discrete spaces""; ""3. The Sierpinski space""; ""4. Pullbacks and projective limits""; ""5. The splitting space""; ""Chapter V � Open maps of spaces""; ""1. Open maps - definition""; ""2. Open subspaces""; ""3. Conditions for openness""; ""4. Open surjections, pullbacks""; ""5. A characterization of discrete spaces""; ""Chapter VI � Change of base""; ""1. Change of base for sup�lattices and locales""; ""2. Determination of sl(S�[sup(Aop)] ) and loc(S�[sup(Aop)] )"" |
| Record Nr. | UNINA-9910480748803321 |
|
Joyal André
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1984 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An extension of the Galois theory of Grothendieck / / André Joyal, Myles Tierney
| An extension of the Galois theory of Grothendieck / / André Joyal, Myles Tierney |
| Autore | Joyal André |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1984 |
| Descrizione fisica | 1 online resource (87 p.) |
| Disciplina | 512/.32 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Toposes
Galois theory Theory of descent (Mathematics) |
| ISBN | 1-4704-0722-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""Introduction""; ""Chapter I � Sup�lattices""; ""1. Definitions and duality""; ""2. Limits and colimits""; ""3. Free sup�lattices""; ""4. Sub and quotient lattices""; ""5. Tensor products""; ""Chapter II � Rings, modules and descent""; ""1. Rings and modules""; ""2. Tensor product of modules""; ""3. Change of rings""; ""4. Flatness, projectivity, and purity""; ""5. Descent theory for modules""; ""Chapter III � Locales""; ""1. Locales and commutative monoids""; ""2. Limits and colimits""; ""3. The free locale""; ""4. Local operators and quotients""
""5. The splitting locale""""Chapter IV � Spaces""; ""1. Subspaces""; ""2. Points and discrete spaces""; ""3. The Sierpinski space""; ""4. Pullbacks and projective limits""; ""5. The splitting space""; ""Chapter V � Open maps of spaces""; ""1. Open maps - definition""; ""2. Open subspaces""; ""3. Conditions for openness""; ""4. Open surjections, pullbacks""; ""5. A characterization of discrete spaces""; ""Chapter VI � Change of base""; ""1. Change of base for sup�lattices and locales""; ""2. Determination of sl(S�[sup(Aop)] ) and loc(S�[sup(Aop)] )"" |
| Record Nr. | UNINA-9910788888603321 |
|
Joyal André
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1984 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An extension of the Galois theory of Grothendieck / / André Joyal, Myles Tierney
| An extension of the Galois theory of Grothendieck / / André Joyal, Myles Tierney |
| Autore | Joyal André |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1984 |
| Descrizione fisica | 1 online resource (87 p.) |
| Disciplina | 512/.32 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Toposes
Galois theory Theory of descent (Mathematics) |
| ISBN | 1-4704-0722-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Table of Contents""; ""Introduction""; ""Chapter I � Sup�lattices""; ""1. Definitions and duality""; ""2. Limits and colimits""; ""3. Free sup�lattices""; ""4. Sub and quotient lattices""; ""5. Tensor products""; ""Chapter II � Rings, modules and descent""; ""1. Rings and modules""; ""2. Tensor product of modules""; ""3. Change of rings""; ""4. Flatness, projectivity, and purity""; ""5. Descent theory for modules""; ""Chapter III � Locales""; ""1. Locales and commutative monoids""; ""2. Limits and colimits""; ""3. The free locale""; ""4. Local operators and quotients""
""5. The splitting locale""""Chapter IV � Spaces""; ""1. Subspaces""; ""2. Points and discrete spaces""; ""3. The Sierpinski space""; ""4. Pullbacks and projective limits""; ""5. The splitting space""; ""Chapter V � Open maps of spaces""; ""1. Open maps - definition""; ""2. Open subspaces""; ""3. Conditions for openness""; ""4. Open surjections, pullbacks""; ""5. A characterization of discrete spaces""; ""Chapter VI � Change of base""; ""1. Change of base for sup�lattices and locales""; ""2. Determination of sl(S�[sup(Aop)] ) and loc(S�[sup(Aop)] )"" |
| Record Nr. | UNINA-9910827403603321 |
|
Joyal André
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1984 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups [[electronic resource]]
| Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups [[electronic resource]] |
| Autore | Rognes John |
| Pubbl/distr/stampa | Providence, : American Mathematical Society, 2008 |
| Descrizione fisica | 1 online resource (154 p.) |
| Disciplina | 512/.32 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Commutative algebra
Galois theory Homology theory Homotopy theory Ring extensions (Algebra) Mathematics Physical Sciences & Mathematics Algebra |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0504-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Galois Extensions of Structured Ring Spectra""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. Galois extensions in algebra""; ""Â2.1. Galois extensions of fields""; ""Â2.2. Regular covering spaces""; ""Â2.3. Galois extensions of commutative rings""; ""Chapter 3. Closed categories of structured module spectra""; ""Â3.1. Structured spectra""; ""Â3.2. Localized categories""; ""Â3.3. Dualizable spectra""; ""Â3.4. Stably dualizable groups""; ""Â3.5. The dualizing spectrum""; ""Â3.6. The norm map""; ""Chapter 4. Galois extensions in topology""
""Â4.1. Galois extensions of E-local commutative S-algebras""""Â4.2. The Eilenberg-Mac Lane embedding""; ""Â4.3. Faithful extensions""; ""Chapter 5. Examples of Galois extensions""; ""Â5.1. Trivial extensions""; ""Â5.2. Eilenberg-Mac Lane spectra""; ""Â5.3. Real and complex topological K-theory""; ""Â5.4. The Morava change-of-rings theorem ""; ""Â5.5. The K(1)-local case ""; ""Â5.6. Cochain S-algebras ""; ""Chapter 6. Dualizability and alternate characterizations""; ""Â6.1. Extended equivalences""; ""Â6.2. Dualizability""; ""Â6.3. Alternate characterizations"" ""Chapter 10. Mapping spaces of commutative S-algebras""""Â10.1. Obstruction theory""; ""Â10.2. Idempotents and connected S-algebras""; ""Â10.3. Separable closure""; ""Chapter 11. Galois theory II""; ""Â11.1. Recovering the Galois group""; ""Â11.2. The brave new Galois correspondence""; ""Chapter 12. Hopfâ€?Galois extensions in topology""; ""Â12.1. Hopfâ€?Galois extensions of commutative S-algebras""; ""Â12.2. Complex cobordism""; ""References""; ""Stably Dualizable Groups""; ""Abstract""; ""Chapter 1. Introduction""; ""Â1.1. The symmetry groups of stable homotopy theory"" ""Â4.3. Eilenberg-Mac Lane spaces"" |
| Record Nr. | UNINA-9910480228703321 |
|
Rognes John
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| Providence, : American Mathematical Society, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
