1989, ISBN: 0387966714
[EAN: 9780387966717], Neubuch, [PU: Springer New York Dez 1989], ZAHLENTHEORIE; PRIME; ALGEBRA; FINITEFIELD; HOMOMORPHISM; NUMBERTHEORY; COHOMOLOGY, This item is printed on demand - it ta… More...
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ISBN: 9780387966717
[ED: Hardcover], [PU: Springer / Springer New York / Springer, Berlin], Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedek… More...
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1989, ISBN: 0387966714
[EAN: 9780387966717], Neubuch, [SC: 0.0], [PU: Springer New York], ZAHLENTHEORIE; PRIME; ALGEBRA; FINITEFIELD; HOMOMORPHISM; NUMBERTHEORY; COHOMOLOGY, Druck auf Anfrage Neuware - Printed … More...
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Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the succ… More...
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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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1989, ISBN: 0387966714
[EAN: 9780387966717], Neubuch, [PU: Springer New York Dez 1989], ZAHLENTHEORIE; PRIME; ALGEBRA; FINITEFIELD; HOMOMORPHISM; NUMBERTHEORY; COHOMOLOGY, This item is printed on demand - it ta… More...
ISBN: 9780387966717
[ED: Hardcover], [PU: Springer / Springer New York / Springer, Berlin], Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedek… More...
1989
ISBN: 0387966714
[EAN: 9780387966717], Neubuch, [SC: 0.0], [PU: Springer New York], ZAHLENTHEORIE; PRIME; ALGEBRA; FINITEFIELD; HOMOMORPHISM; NUMBERTHEORY; COHOMOLOGY, Druck auf Anfrage Neuware - Printed … More...
ISBN: 9780387966717
Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the succ… More...
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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Details of the book - Cyclotomic Fields I and II Serge Lang Author
EAN (ISBN-13): 9780387966717
ISBN (ISBN-10): 0387966714
Hardcover
Paperback
Publishing year: 2007
Publisher: Springer New York Core >2 >T
458 Pages
Weight: 0,877 kg
Language: eng/Englisch
Book in our database since 2007-05-28T13:44:13+01:00 (London)
Detail page last modified on 2024-03-31T11:43:33+01:00 (London)
ISBN/EAN: 9780387966717
ISBN - alternate spelling:
0-387-96671-4, 978-0-387-96671-7
Alternate spelling and related search-keywords:
Book author: karl lang, serge lang
Book title: graduate texts mathematics, the fields, cyclotomic fields and
Information from Publisher
Author: Serge Lang
Title: Graduate Texts in Mathematics; Cyclotomic Fields I and II
Publisher: Springer; Springer US
436 Pages
Publishing year: 1989-12-18
New York; NY; US
Language: English
90,94 € (DE)
93,49 € (AT)
100,50 CHF (CH)
Available
XVII, 436 p.
BB; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Zahlentheorie; Verstehen; Cohomology; Prime; algebra; finite field; homomorphism; number theory; Number Theory; BC
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. AnalyticRepresentation 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.More/other books that might be very similar to this book
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