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Field Arithmetic
| Field Arithmetic |
| Autore | Fried Michael D |
| Edizione | [4th ed.] |
| Pubbl/distr/stampa | Cham : , : Springer, , 2023 |
| Descrizione fisica | 1 online resource (839 pages) |
| Disciplina | 658.40301 |
| Altri autori (Persone) | JardenMoshe |
| Collana | Ergebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge / a Series of Modern Surveys in Mathematics Series |
| ISBN | 3-031-28020-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface to the Fourth Edition -- Main New Results -- Detailed List of New Results -- Problems of Field Arithmetic -- Structural Changes -- Typing Programs -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Notation and Conventions -- Contents -- Chapter 1 Infinite Galois Theory and Profinite Groups -- 1.1 Inverse Limits -- 1.2 Profinite Groups -- 1.3 Infinite Galois Theory -- 1.4 The -adic Integers and the Prüfer Group -- 1.5 The Absolute Galois Group of a Finite Field -- Exercises -- Notes -- Chapter 2 Valuations -- 2.1 Valuations, Places, and Valuation Rings -- 2.2 Discrete Valuations -- 2.3 Extensions of Valuations and Places -- 2.4 Galois Extensions -- 2.5 Integral Extensions and Dedekind Domains -- Exercises -- Chapter 3 Linear Disjointness -- 3.1 Linear Disjointness of Fields -- 3.2 Purely Transcendental Extensions -- 3.3 Separable Extensions -- 3.4 Regular Extensions -- 3.5 Primary Extensions -- 3.6 The Imperfect Degree of a Field -- 3.7 Derivatives -- Exercises -- Chapter 4 Algebraic Function Fields of One Variable -- 4.1 Function Fields of One Variable -- 4.2 The Riemann-Roch Theorem -- 4.3 Holomorphy Rings -- 4.4 Extensions of Function Fields -- 4.5 Completions -- 4.6 The Different -- 4.7 Hyperelliptic Fields -- 4.8 Hyperelliptic Fields with a Rational Quadratic Subfield -- Exercises -- Notes -- Chapter 5 The Riemann Hypothesis for Function Fields -- 5.1 Class Numbers -- 5.2 Zeta Functions -- 5.3 Zeta Functions under Constant Field Extensions -- 5.4 The Functional Equation -- 5.5 The Riemann Hypothesis and Degree 1 Prime Divisors -- 5.6 Reduction Steps -- 5.7 An Upper Bound -- 5.8 A Lower Bound -- Exercises -- Notes -- Chapter 6 Plane Curves -- 6.1 Affine and Projective Plane Curves -- 6.2 Points and Prime Divisors -- 6.3 The Genus of a Plane Curve.
6.4 Points on a Curve over a Finite Field -- Exercises -- Notes -- Chapter 7 The Chebotarev Density Theorem -- 7.1 Decomposition Groups -- 7.2 The Artin Symbol over Global Fields -- 7.3 Dirichlet Density -- 7.4 Function Fields -- 7.5 Number Fields -- Exercises -- Notes -- Chapter 8 Ultraproducts -- 8.1 First Order Predicate Calculus -- 8.2 Structures -- 8.3 Models -- 8.4 Elementary Substructures -- 8.5 Ultrafilters -- 8.6 Ultraproducts -- 8.7 Regular Ultrafilters -- 8.8 Regular Ultraproducts -- 8.9 Nonprincipal Ultraproducts of Finite Fields -- Exercises -- Notes -- Chapter 9 Decision Procedures -- 9.1 Deduction Theory -- 9.2 Gödel's Completeness Theorem -- 9.3 Primitive Recursive Functions -- 9.4 Primitive Recursive Relations -- 9.5 Recursive Functions -- 9.6 Recursive and Primitive Recursive Procedures -- 9.7 A Reduction Step in Decidability Procedures -- Exercises -- Notes -- Chapter 10 Algebraically Closed Fields -- 10.1 Elimination of Quantifiers -- 10.2 A Quantifier Elimination Procedure -- 10.3 Effectiveness -- 10.4 Applications -- Exercises -- Notes -- Chapter 11 Elements of Algebraic Geometry -- 11.1 Algebraic Sets -- 11.2 Varieties -- 11.3 Substitutions in Irreducible Polynomials -- 11.4 Rational Maps -- 11.5 Hyperplane Sections -- 11.6 Descent -- 11.7 Projective Varieties -- 11.8 About the Language of Algebraic Geometry -- Exercises -- Notes -- Chapter 12 Pseudo Algebraically Closed Fields -- 12.1 PAC Fields -- 12.2 Reduction to Plane Curves -- 12.3 The PAC Property is an Elementary Statement -- 12.4 PAC Fields of Positive Characteristic -- 12.5 PAC Fields with Valuations -- 12.6 The Absolute Galois Group of a PAC Field -- 12.7 A non-PAC Field with ins PAC -- Exercises -- Notes -- Chapter 13 Hilbertian Fields -- 13.1 Hilbert Sets and Reduction Lemmas -- 13.2 Hilbert Sets under Separable Algebraic Extensions. 13.3 Purely Inseparable Extensions -- 13.4 Imperfect Fields -- Exercises -- Notes -- Chapter 14 The Classical Hilbertian Fields -- 14.1 Further Reduction -- 14.2 Function Fields Over Infinite Fields -- 14.3 Global Fields -- 14.4 Hilbertian Rings -- 14.5 Hilbertianity via Coverings -- 14.6 Non-Hilbertian -Hilbertian Fields -- Exercises -- Notes -- Chapter 15 The Diamond Theorem -- 15.1 Twisted Wreath Products -- 15.2 The Diamond Theorem -- 15.3 Weissauer's Theorem -- Exercises -- Notes -- Chapter 16 Nonstandard Structures -- 16.1 Higher Order Predicate Calculus -- 16.2 Enlargements -- 16.3 Concurrent Relations -- 16.4 The Existence of Enlargements -- 16.5 Examples -- Exercises -- Notes -- Chapter 17 The Nonstandard Approach to Hilbert's Irreducibility Theorem -- 17.1 Criteria for Hilbertianity -- 17.2 Arithmetical Primes Versus Functional Primes -- 17.3 Fields with the Product Formula -- 17.4 Generalized Krull Domains -- 17.5 Examples -- Exercises -- Notes -- Chapter 18 Galois Groups over Hilbertian Fields -- 18.1 Galois Groups of Polynomials -- 18.2 Stable Polynomials -- 18.3 Regular Realization of Finite Abelian Groups -- 18.4 Split Embedding Problems with Abelian Kernels -- 18.5 Embedding Quadratic Extensions in Z/2 Z-Extensions -- 18.6 Z -Extensions of Hilbertian Fields -- 18.7 Symmetric and Alternating Groups over Hilbertian Fields -- 18.8 GAR-Realizations -- 18.9 Embedding Problems over Hilbertian Fields -- 18.10 Regularity of Finite Groups over Complete Discrete-Valued Fields -- Exercises -- Notes -- Chapter 19 Small Profinite Groups -- 19.1 Finitely Generated Profinite Groups -- 19.2 Abelian Extensions of Hilbertian Fields -- Exercises -- Notes -- Chapter 20 Free Profinite Groups -- 20.1 The Rank of a Profinite Group -- 20.2 Profinite Completions of Groups -- 20.3 Formations of Finite Groups -- 20.4 Free pro-C Groups. 20.5 Subgroups of Free Discrete Groups -- 20.6 Open Subgroups of Free Profinite Groups -- 20.7 An Embedding Property -- Exercises -- Notes -- Chapter 21 The Haar Measure -- 21.1 The Haar Measure of a Profinite Group -- 21.2 Existence of the Haar Measure -- 21.3 Independence -- 21.4 Cartesian Product of Haar Measures -- 21.5 The Haar Measure of the Absolute Galois Group -- 21.6 The PAC Nullstellensatz -- 21.7 Baire's Theorem -- 21.8 The Bottom Theorem -- 21.9 Triviality of a Group of Automorphisms -- 21.10 PAC Fields over Uncountable Hilbertian Fields -- 21.11 On the Stability of Fields -- 21.12 PAC Galois Extensions of Hilbertian Fields -- 21.13 Algebraic Groups -- Exercises -- Notes -- Chapter 22 Effective Field Theory and Algebraic Geometry -- 22.1 Presented Rings and Fields -- 22.2 Extensions of Presented Fields -- 22.3 Galois Extensions of Presented Fields -- 22.4 The Algebraic and Separable Closures of Presented Fields -- 22.5 Constructive Algebraic Geometry -- 22.6 Presented Rings and Constructible Sets -- 22.7 Basic Normal Stratification -- Exercises -- Notes -- Chapter 23 The Elementary Theory of -Free PAC Fields -- 23.1 ℵ1-Saturated PAC Fields -- 23.2 The Elementary Equivalence Theorem of ℵ1-Saturated PAC Fields -- 23.3 Elementary Equivalence of PAC Fields -- 23.4 On On -Free PAC Fields -- 23.5 The Elementary Theory of Perfect -Free PAC Fields -- 23.6 The Probable Truth of a Sentence -- 23.7 Change of Base Field -- 23.8 The Fields sep( 1, . . . , ) -- 23.9 The Transfer Theorem -- 23.10 The Elementary Theory of Finite Fields -- Exercises -- Notes -- Chapter 24 Problems of Arithmetical Geometry -- 24.1 The Decomposition-Intersection Procedure -- 24.2 -Fields and Weakly -Fields -- 24.3 Perfect PAC Fields which are -- 24.4 The Existential Theory of PAC Fields -- 24.5 Kronecker Classes of Number Fields -- 24.6 Davenport's Problem. 24.7 On Permutation Groups -- 24.8 Schur's Conjecture -- 24.9 The Generalized Carlitz Conjecture -- Exercises -- Notes -- Chapter 25 Projective Groups and Frattini Covers -- 25.1 The Frattini Group of a Profinite Group -- 25.2 Cartesian Squares -- 25.3 On On C-Projective Groups -- 25.4 Projective Groups -- 25.5 Free Products of Finitely many Profinite Groups -- 25.6 Frattini Covers -- 25.7 The Universal Frattini Cover -- 25.8 Projective Pro- -Groups -- 25.9 Supernatural Numbers -- 25.10 The Sylow Theorems -- 25.11 On Complements of Normal Subgroups -- 25.12 The Universal Frattini -Cover -- 25.13 Examples of Universal Frattini -covers -- 25.14 The Special Linear Group SL(2, Z ) -- 25.15 The General Linear Group GL(2, Z ) -- 25.16 Absolute Galois Groups -- Exercises -- Notes -- Chapter 26 PAC Fields and Projective Absolute Galois Groups -- 26.1 Projective Groups as Absolute Galois Groups -- 26.2 Countably Generated Projective Groups -- 26.3 Perfect PAC Fields of Bounded Corank -- 26.4 Basic Elementary Statements -- 26.5 Reduction Steps -- 26.6 Application of Ultraproducts -- Exercises -- Notes -- Chapter 27 Frobenius Fields -- 27.1 The Field Crossing Argument -- 27.2 The Beckmann-Black Problem -- 27.3 The Embedding Property and Maximal Frattini Covers -- 27.4 The Smallest Embedding Cover of a Profinite Group -- 27.5 A Decision Procedure -- 27.6 Examples -- 27.7 Non-projective Smallest Embedding Cover -- 27.8 A Theorem of Iwasawa -- 27.9 Free Profinite Groups of Countable Rank -- 27.10 Application of the Nielsen-Schreier Formula -- Exercises -- Notes -- Chapter 28 Free Profinite Groups of Infinite Rank -- 28.1 Characterization of Free Profinite Groups by Embedding Problems -- 28.2 Applications of Theorem 28.1.7 -- 28.3 The Pro-Completion of a Free Discrete Group -- 28.4 The Group Theoretic Diamond Theorem. 28.5 The Melnikov Group of a Profinite Group. |
| Record Nr. | UNINA-9910731456903321 |
Fried Michael D
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| Cham : , : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Field arithmetic / M. D. Fried, M. Jarden
| Field arithmetic / M. D. Fried, M. Jarden |
| Autore | Fried, Michael D. |
| Pubbl/distr/stampa | Berlin : Springer, c2008 |
| Descrizione fisica | XXIII, 792 p. ; 24 cm |
| Disciplina | 512.3 |
| Altri autori (Persone) | Jarden, Moshe |
| Collana | Series of modern surveys in mathematics |
| Soggetto non controllato |
Campi algebrici
Teoria dei numeri algebrici |
| ISBN | 978-3-540-77269-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Revised by Mosche Jarden |
| Record Nr. | UNINA-990008684520403321 |
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Fried, Michael D.
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| Berlin : Springer, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Field arithmetic / Michael D. Fried, Moshe Jarden : Second edition revised and enlarged by Moshe Jarden
| Field arithmetic / Michael D. Fried, Moshe Jarden : Second edition revised and enlarged by Moshe Jarden |
| Autore | FRIED, Michael |
| Edizione | [2 ed.] |
| Pubbl/distr/stampa | Berlin [etc.] : Springer, copyr. 2004 |
| Descrizione fisica | XXII, 780 p. ; 24 cm |
| Disciplina | 512.3 |
| Altri autori (Persone) | JARDEN, Moshe |
| Collana | Ergebnisse der mathematik und ihre grenzgebiete. 3 folge |
| Soggetto topico | Campi algebrici |
| ISBN | 3-540-22811-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-990003123480203316 |
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FRIED, Michael
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| Berlin [etc.] : Springer, copyr. 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Field arithmetic / Michael D. Fried, Moshe Jarden
| Field arithmetic / Michael D. Fried, Moshe Jarden |
| Autore | FRIED, Michael |
| Pubbl/distr/stampa | Berlin : Springer Verlag, c1986 |
| Descrizione fisica | XVI, 458 p. ; 24 cm |
| Disciplina | 512.3 |
| Altri autori (Persone) | JARDEN, Moshe |
| Collana | Ergebnisse der Mathematik und Ihre Grenzgebiete. 3 folge |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-990000632800203316 |
|
FRIED, Michael
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| Berlin : Springer Verlag, c1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Field arithmetic / Michael D. Fried, Moshe Jarden
| Field arithmetic / Michael D. Fried, Moshe Jarden |
| Autore | Fried, Michael D. <1942- > |
| Pubbl/distr/stampa | Berlin, : Springer, 1986 |
| Descrizione fisica | XVI, 458 p. : ill. ; 25 cm. |
| Altri autori (Persone) | Jarden, Moshe |
| Soggetto topico | 12-XX - Field theory and polynomials [MSC 2020] |
| ISBN |
35-401-6640-8
8-3540166405 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-SUN0029659 |
|
Fried, Michael D. <1942- >
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||
| Berlin, : Springer, 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Field arithmetic / Michael D. Fried, Moshe Jarden
| Field arithmetic / Michael D. Fried, Moshe Jarden |
| Autore | Fried, Michael D. <1942- > |
| Pubbl/distr/stampa | Berlin, : Springer, 1986 |
| Descrizione fisica | XVI, 458 p. : ill. ; 25 cm |
| Altri autori (Persone) | Jarden, Moshe |
| Soggetto topico | 12-XX - Field theory and polynomials [MSC 2020] |
| Soggetto non controllato |
Absolute Galois Groups
Algebra Algebraic Geometry Finite Groups Galois Stratification Galois groups Galois theory Hilbertian Fields Irreducibility PAC Fields Profinite groups ultraproductS |
| ISBN | 978-35-401-6640-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0029659 |
|
Fried, Michael D. <1942- >
|
||
| Berlin, : Springer, 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Field arithmetic / Michael D. Fried, Moshe Jarden
| Field arithmetic / Michael D. Fried, Moshe Jarden |
| Autore | Fried, Michael D. <1942- > |
| Pubbl/distr/stampa | Berlin, : Springer, 1986 |
| Descrizione fisica | xvi, 458 p. : ill. ; 25 cm |
| Altri autori (Persone) | Jarden, Moshe |
| Soggetto topico |
12-XX - Field theory and polynomials [MSC 2020]
14G05 - Rational points [MSC 2020] 12E25 - Hilbertian fields; Hilbert's irreducibility theorem [MSC 2020] 03C60 - Model-theoretic algebra [MSC 2020] 03H15 - Nonstandard models of arithmetic [MSC 2020] 03C20 - Ultraproducts and related constructions [MSC 2020] 12E30 - Field arithmetic [MSC 2020] 03C10 - Quantifier elimination, model completeness and related topics [MSC 2020] 12L12 - Model theory of fields [MSC 2020] 12L15 - Nonstandard arithmetic and field theory [MSC 2020] 12L05 - Decidability and field theory [MSC 2020] |
| Soggetto non controllato |
Absolute Galois Groups
Algebra Algebraic Geometry Finite Groups Galois Stratification Galois groups Galois theory Hilbertian Fields Irreducibility PAC Fields Profinite groups ultraproductS |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0263774 |
|
Fried, Michael D. <1942- >
|
||
| Berlin, : Springer, 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Field arithmetic / Michael D. Fried, Moshe Jarden
| Field arithmetic / Michael D. Fried, Moshe Jarden |
| Autore | Fried, Michael D. |
| Pubbl/distr/stampa | Berlin ; New York : Springer-Verlag, c1986 |
| Descrizione fisica | xvi, 458 p. : ill. ; 25 cm. |
| Disciplina | 512.3 |
| Altri autori (Persone) | Jarden, Mosheauthor |
| Soggetto topico |
Algebraic fields
Algebraic number theory |
| ISBN | 3540166408 |
| Classificazione |
AMS 12-02
AMS 12-XX AMS 12L05 AMS 12L10 AMS 12L15 LC QA247.F73 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | en |
| Record Nr. | UNISALENTO-991000887669707536 |
|
Fried, Michael D.
|
||
| Berlin ; New York : Springer-Verlag, c1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Field arithmetic / M.D.Fried,M.Jarden
| Field arithmetic / M.D.Fried,M.Jarden |
| Edizione | [2nd.edz] |
| Pubbl/distr/stampa | Berlin : Springer, c2005 |
| Descrizione fisica | xxii,780 p. ; 24 cm |
| Disciplina | 512.3 |
| Altri autori (Persone) |
Fried, Michael D.
Jarden, Moshe |
| Collana | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| Soggetto non controllato | Campi algebrici |
| ISBN | 3-540-22811-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-990007977740403321 |
| Berlin : Springer, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The Absolute Galois Group of a Semi-Local Field / Dan Haran, Moshe Jarden
| The Absolute Galois Group of a Semi-Local Field / Dan Haran, Moshe Jarden |
| Autore | Haran, Dan |
| Pubbl/distr/stampa | Cham, : Springer, 2021 |
| Descrizione fisica | xvi, 137 p. : ill. ; 24 cm |
| Altri autori (Persone) | Jarden, Moshe |
| Soggetto non controllato |
Absolute Galois Groups
Embedding problem Field arithmetic Free profinite product of profinite group Haar measure Semi-local fields Strong projectivity |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0275333 |
|
Haran, Dan
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| Cham, : Springer, 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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