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Introduction to algebraic and abelian functions

Author: Serge Lang
Publisher: New York : Springer-Verlag, ©1982.
Series: Graduate texts in mathematics, 89.
Edition/Format:   Book : English : 2nd edView all editions and formats
Database:WorldCat
Summary:

Covers presentation of a fundamental subject in algebraic geometry and number theory. This edition includes the material on theta functions, and the example of the Fermat curves is carried throughout  Read more...

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Additional Physical Format: Online version:
Lang, Serge, 1927-2005.
Introduction to algebraic and abelian functions.
New York : Springer-Verlag, c1982
(OCoLC)812612727
Document Type: Book
All Authors / Contributors: Serge Lang
ISBN: 0387907106 9780387907109 3540907106 9783540907107
OCLC Number: 8410976
Notes: Includes index.
Description: ix, 169 p. ; 25 cm.
Contents: I The Riemann-Roch Theorem.- x1. Lemmas on Valuations.- x2. The Riemann-Roch Theorem.- x3. Remarks on Differential Forms.- x4. Residues in Power Series Fields.- x5. The Sum of the Residues.- x6. The Genus Formula of Hurwitz.- x7. Examples.- x8. Differentials of Second Kind.- x9. Function Fields and Curves.- x10. Divisor Classes.- II The Fermat Curve.- x1. The Genus.- x2. Differentials.- x3. Rational Images of the Fermat Curve.- x4. Decomposition of the Divisor Classes.- III The Riemann Surface.- x1. Topology and Analytic Structure.- x2. Integration on the Riemann Surface.- IV The Theorem of Abel-Jacobi.- x1. Abelian Integrals.- x2. Abel's Theorem.- x3. Jacobi's Theorem.- x4. Riemann's Relations.- x5. Duality.- V Periods on the Fermat Curve.- x1. The Logarithm Symbol.- x2. Periods on the Universal Covering Space.- x3. Periods on the Fermat Curve.- x4. Periods on the Related Curves.- VI Linear Theory of Theta Functions.- x1. Associated Linear Forms.- x2. Degenerate Theta Functions.- x3. Dimension of the Space of Theta Functions.- x4. Abelian Functions and Riemann-Roch Theorem on the Torus.- x5. Translations of Theta Functions.- x6. Projective Embedding.- VII Homomorphisms and Duality.- x1. The Complex and Rational Representations.- x2. Rational and p-adic Representations.- x3. Homomorphisms.- x4. Complete Reducibility of Poincare.- x5. The Dual Abelian Manifold.- x6. Relations with Theta Functions.- x7. The Kummer Pairing.- x8. Periods and Homology.- VIII Riemann Matrices and Classical Theta Functions.- x1. Riemann Matrices.- x2. The Siegel Upper Half Space.- x3. Fundamental Theta Functions.- IX Involutions and Abelian Manifolds of Quaternion Type.- x1. Involutions.- x2. Special Generators.- x3. Orders.- x4. Lattices and Riemann Forms on C2 Determined by Quaternion Algebras.- x5. Isomorphism Classes.- X Theta Functions and Divisors.- x1. Positive Divisors.- x2. Arbitrary Divisors.- x3. Existence of a Riemann Form on an Abelian Variety.
Series Title: Graduate texts in mathematics, 89.
Responsibility: Serge Lang.
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Second Edition S. Lang Introduction to Algebraic and Abelian Functions "An excellent and very readable introduction to basic notions in algebraic geometry."-MATHEMATICAL REVIEWS

 
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