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Cyclotomic Fields I and II / Serge Lang / Buch / Graduate Texts in Mathematics / HC runder Rücken kaschiert / xvii / Englisch / 1989 / Springer US / EAN 9780387966717 - Lang, Serge
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Lang, Serge:

Cyclotomic Fields I and II / Serge Lang / Buch / Graduate Texts in Mathematics / HC runder Rücken kaschiert / xvii / Englisch / 1989 / Springer US / EAN 9780387966717 - encuadernado, tapa blanda

1989, ISBN: 9780387966717

[ED: Gebunden], [PU: Springer US], Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, … Más…

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Cyclotomic Fields I and II | Serge Lang | Buch | Graduate Texts in Mathematics | HC runder Rücken kaschiert | xvii | Englisch | 1989 | Springer US | EAN 9780387966717 - Lang, Serge
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Lang, Serge:

Cyclotomic Fields I and II | Serge Lang | Buch | Graduate Texts in Mathematics | HC runder Rücken kaschiert | xvii | Englisch | 1989 | Springer US | EAN 9780387966717 - encuadernado, tapa blanda

1989, ISBN: 9780387966717

[ED: Gebunden], [PU: Springer US], Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, … Más…

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Cyclotomic Fields I and II (Graduate Texts in Mathematics, 121, Band 121) - Lang, Serge
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Lang, Serge:
Cyclotomic Fields I and II (Graduate Texts in Mathematics, 121, Band 121) - encuadernado, tapa blanda

1989

ISBN: 9780387966717

Assistent: Rubin, Karl, Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1990, 453 Seiten, Publiziert: 1989-12-18T00:00:01Z, Produktgruppe: Buch, 3.99 kg, Verkaufsrang: 2828167, Algebra & Za… Más…

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Cyclotomic Fields I and II - Serge Lang
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Serge Lang:
Cyclotomic Fields I and II - encuadernado, tapa blanda

1989, ISBN: 9780387966717

[ED: Gebunden], [PU: Springer New York], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Kummer s work on cyclotomic fields paved the way … Más…

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Cyclotomic Fields I and II - Lang, Serge
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Lang, Serge:
Cyclotomic Fields I and II - encuadernado, tapa blanda

1989, ISBN: 0387966714

2nd ed. 1990 Gebundene Ausgabe Zahlentheorie, Prime; Algebra; finitefield; homomorphism; numbertheory; cohomology, mit Schutzumschlag 11, [PU:Springer New York; Springer US]

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Detalles del libro
Cyclotomic Fields I and II (Graduate Texts in Mathematics, 121, Band 121)

This book is a combined edition of the books previously published as Cyclotomic Fields, Vol. I and II. It continues to provide a basic introduction to the theory of these number fields, which are of great interest in classical number theory, as well as in other areas, such as K-theory. Cyclotomic Fields begins with basic material on character sums, and proceeds to treat class number formulas, p-adic L-functions, Iwasawa theory, Lubin-Tate theory, and explicit reciprocity laws, and the Ferrero-Washington theorems, which prove Iwasawa's conjecture on the growth of the p-primary part of the ideal class group.

Detalles del libro - Cyclotomic Fields I and II (Graduate Texts in Mathematics, 121, Band 121)


EAN (ISBN-13): 9780387966717
ISBN (ISBN-10): 0387966714
Tapa dura
Tapa blanda
Año de publicación: 2007
Editorial: Springer
458 Páginas
Peso: 0,877 kg
Idioma: eng/Englisch

Libro en la base de datos desde 2007-05-28T07:44:13-05:00 (Mexico City)
Página de detalles modificada por última vez el 2024-02-04T08:33:54-06:00 (Mexico City)
ISBN/EAN: 9780387966717

ISBN - escritura alterna:
0-387-96671-4, 978-0-387-96671-7
Mode alterno de escritura y términos de búsqueda relacionados:
Autor del libro: karl lang, serge lang
Título del libro: graduate texts mathematics, the fields, cyclotomic fields and


Datos del la editorial

Autor: Serge Lang
Título: Graduate Texts in Mathematics; Cyclotomic Fields I and II
Editorial: Springer; Springer US
436 Páginas
Año de publicación: 1989-12-18
New York; NY; US
Peso: 1,810 kg
Idioma: Inglés
90,94 € (DE)
93,49 € (AT)
100,50 CHF (CH)
POD
XVII, 436 p.

BB; Number Theory; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Zahlentheorie; Verstehen; Cohomology; Prime; algebra; finite field; homomorphism; number theory; Number Theory; BB; BC; EA

1 Character Sums.- 1. Character Sums over Finite Fields.- 2. Stickelberger’s Theorem.- 3. Relations in the Ideal Classes.- 4. Jacobi Sums as Hecke Characters.- 5. Gauss Sums over Extension Fields.- 6. Application to the Fermat Curve.- 2 Stickelberger Ideals and Bernoulli Distributions.- 1. The Index of the First Stickelberger Ideal.- 2. Bernoulli Numbers.- 3. Integral Stickelberger Ideals.- 4. General Comments on Indices.- 5. The Index for k Even.- 6. The Index for k Odd.- 7. Twistings and Stickelberger Ideals.- 8. Stickelberger Elements as Distributions.- 9. Universal Distributions.- 10. The Davenport-Hasse Distribution.- Appendix. Distributions.- 3 Complex Analytic Class Number Formulas.- 1. Gauss Sums on Z/mZ.- 2. Primitive L-series.- 3. Decomposition of L-series.- 4. The (± 1)-eigenspaces.- 5. Cyclotomic Units.- 6. The Dedekind Determinant.- 7. Bounds for Class Numbers.- 4 The p-adic L-function.- 1. Measures and Power Series.- 2. Operations on Measures and Power Series.- 3. The Mellin Transform and p-adic L-function.- Appendix. The p-adic Logarithm.- 4. The p-adic Regulator.- 5. The Formal Leopoldt Transform.- 6. The p-adic Leopoldt Transform.- 5 Iwasawa Theory and Ideal Class Groups.- 1. The Iwasawa Algebra.- 2. Weierstrass Preparation Theorem.- 3. Modules over ZP[[X]].- 4. Zp-extensions and Ideal Class Groups.- 5. The Maximal p-abelian p-ramified Extension.- 6. The Galois Group as Module over the Iwasawa Algebra.- 6 Kummer Theory over Cyclotomic Zp-extensions.- 1. The Cyclotomic Zp-extension.- 2. The Maximal p-abelian p-ramified Extension of the Cyclotomic Zp-extension.- 3. Cyclotomic Units as a Universal Distribution.- 4. The Iwasawa-Leopoldt Theorem and the Kummer-Vandiver Conjecture.- 7 Iwasawa Theory of Local Units.- 1. The Kummer-Takagi Exponents.- 2. Projective Limit of the Unit Groups.- 3. A Basis for U(x) over A.- 4. The Coates-Wiles Homomorphism.- 5. The Closure of the Cyclotomic Units.- 8 Lubin-Tate Theory.- 1. Lubin-Tate Groups.- 2. Formal p-adic Multiplication.- 3. Changing the Prime.- 4. The Reciprocity Law.- 5. The Kummer Pairing.- 6. The Logarithm.- 7. Application of the Logarithm to the Local Symbol.- 9 Explicit Reciprocity Laws.- 1. Statement of the Reciprocity Laws.- 2. The Logarithmic Derivative.- 3. A Local Pairing with the Logarithmic Derivative.- 4. The Main Lemma for Highly Divisible x and ? = xn.- 5. The Main Theorem for the Symbol ?x, xn?n.- 6. The Main Theorem for Divisible x and ? = unit.- 7. End of the Proof of the Main Theorems.- 10 Measures and Iwasawa Power Series.- 1. Iwasawa Invariants for Measures.- 2. Application to the Bernoulli Distributions.- 3. Class Numbers as Products of Bernoulli Numbers.- Appendix by L. Washington: Probabilities.- 4. Divisibility by l Prime to p: Washington’s Theorem.- 11 The Ferrero-Washington Theorems.- 1. Basic Lemma and Applications.- 2. Equidistribution and Normal Families.- 3. An Approximation Lemma.- 4. Proof of the Basic Lemma.- 12 Measures in the Composite Case.- 1. Measures and Power Series in the Composite Case.- 2. The Associated Analytic Function on the Formal Multiplicative Group.- 3. Computation of Lp(1, x) in the Composite Case.- 13 Divisibility of Ideal Class Numbers.- 1. Iwasawa Invariants in Zp-extensions.- 2. CM Fields, Real Subfields, and Rank Inequalities.- 3. The l-primary Part in an Extension of Degree Prime to l.- 4. A Relation between Certain Invariants in a Cyclic Extension.- 5. Examples of Iwasawa.- 6. A Lemma of Kummer.- 14 P-adic Preliminaries.- 1. The p-adic Gamma Function.- 2. The Artin-Hasse Power Series.- 3. Analytic Representation of Roots of Unity.- Appendix: Barsky’s Existence Proof for the p-adic Gamma Function.- 15 The Gamma Function and Gauss Sums.- 1. The Basic Spaces.- 2. The Frobenius Endomorphism.- 3. The Dwork Trace Formula and Gauss Sums.- 4. Eigenvalues of the Frobenius Endomorphism and the p-adic Gamma Function.- 5. p-adic Banach Spaces.- 16 Gauss Sums and the Artin-Schreier Curve.- 1. Power Series with Growth Conditions.- 2. The Artin-Schreier Equation.- 3. Washnitzer-Monsky Cohomology.- 4. The Frobenius Endomorphism.- 17 Gauss Sums as Distributions.- 1. The Universal Distribution.- 2. The Gauss Sums as Universal Distributions.- 3. The L-function at s = 0.- 4. The p-adic Partial Zeta Function.- Appendix by Karl Rubin.- The Main Conjecture.- 1. Setting and Notation.- 2. Properties of Kolyvagin’s “Euler System”.- 3. An Application of the Chebotarev Theorem.- 5. The Main Conjecture.- 6. Tools from Iwasawa Theory.- 7. Proof of Theorem 5.1.- 8. Other Formulations and Consequences of the Main Conjecture.

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