Basic Structures of Function Field Arithmetic Goss, David: - used book

EAN (ISBN-13): 9783540610878
ISBN (ISBN-10): 3540610871
Hardcover
Publishing year: 1996
Publisher: Springer

Book in our database since 2012-03-19T01:07:33+00:00 (London)
Detail page last modified on 2024-01-16T15:16:52+00:00 (London)
ISBN/EAN: 9783540610878

ISBN - alternate spelling:
3-540-61087-1, 978-3-540-61087-8
Alternate spelling and related search-keywords:
Book author: goss david
Book title: basic structures, arithmetic function fields, surveys modern mathematics, structure arithmetic, mathematik

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Information from Publisher

Author: David Goss
Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge; Basic Structures of Function Field Arithmetic - A Series of Modern Surveys in Mathematics
Publisher: Springer; Springer Berlin
424 Pages
Publishing year: 1996-10-17
Berlin; Heidelberg; DE
Printed / Made in
Weight: 0,770 kg
Language: English
85,55 € (DE)
87,95 € (AT)
106,60 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Zahlentheorie; Verstehen; algebraic number theory; calculus; number theory; finite field; zeta function; Dimension; Grad; algebraic geometry; Drinfeld module; C; Number Theory; Mathematics and Statistics; Algebraic Geometry; Algebraische Geometrie; BC; EA

1. Additive Polynomials.- 1.1. Basic Properties.- 1.2. Classification of Additive Polynomials.- 1.3. The Moore Determinant.- 1.4. The Relationship Between k[x] and k{?}.- 1.5. The p-resultant.- 1.6. The Left and Right Division Algorithms.- 1.7. The ?-adjoint of an Additive Polynomial.- 1.8. Dividing A1 by Finite Additive Groups.- 1.9. Analogs in Differential Equations/Algebra.- 1.10. Divisibility Theory.- 1.11. The Semi-invariants of Additive Polynomials.- 2. Review of Non-Archimedean Analysis.- 3. The Carlitz Module.- 3.1. Background.- 3.2. The Carlitz Exponential.- 3.3. The Carlitz Module.- 3.4. The Carlitz Logarithm.- 3.5. The Polynomials Ed(x).- 3.6. The Carlitz Module over Arbitrary A-fields.- 3.7. The Adjoint of the Carlitz Module.- 4. Drinfeld Modules.- 4.1. Introduction.- 4.2. Lattices and Their Exponential Functions.- 4.3. The Drinfeld Module Associated to a Lattice.- 4.4. The General Definition of a Drinfeld Module.- 4.5. The Height and Rank of a Drinfeld Module.- 4.6. Lattices and Drinfeld Modules over C?.- 4.7. Morphisms of Drinfeld Modules.- 4.8. Primality in F{?} and A.- 4.9. The Action of Ideals on Drinfeld Modules.- 4.10. The Reduction Theory of Drinfeld Modules.- 4.11. Review of Central Simple Algebra.- 4.12. Drinfeld Modules over Finite Fields.- 4.13. Rigidity of Drinfeld Modules.- 4.14. The Adjoint of a General Drinfeld Module.- 5. T-Modules.- 5.1. Vector Bundles.- 5.2. Sheaves and Differential Equations.- 5.3. ?-sheaves.- 5.4. Basic Concepts of T-modules.- 5.5. Pure T-modules.- 5.6. Torsion Points.- 5.7. Tensor Products.- 5.8. The Tensor Powers of the Carlitz Module.- 5.9. Uniformization.- 5.10. The Tensor Powers of the Carlitz Module redux.- 5.11. Scattering Matrices.- 6. Shtukas.- 6.1. Review of Some Algebraic Geometry.- 6.2. The Shtuka Correspondence.- 7. Sign Normalized Rank 1 Drinfeld Modules.- 7.1. Class-fields as Moduli.- 7.2. Sign Normalization.- 7.3. Fields of Definition of Drinfeld Modules.- 7.4. The Normalizing Field.- 7.5. Division Fields.- 7.6. Principal Ideal Theorems.- 7.7. A Rank One Version of Serre’s Theorem.- 7.8. Classical Partial Zeta Functions.- 7.9. Unit Calculations.- 7.10. Period Computations.- 7.11. The Connection with Shtukas and Examples.- 8. L-series.- 8.1. The “Complex Plane” S?.- 8.2. Exponentiation of Ideals.- 8.3. ?-adic Exponentiation of Ideals.- 8.4. Continuous Functions on ? p.- 8.5. Entire Functions on S?.- 8.6. L-series of Characteristic p Arithmetic.- 8.7. Formal Dirichlet Series.- 8.8. Estimates.- 8.9. L-series of Finite Characters.- 8.10. The Question of Local Factors.- 8.11. The Generalized Teichmüller Character.- 8.12. Special-values at Negative Integers.- 8.13. Trivial Zeroes.- 8.14. Applications to Class Groups.- 8.15. “Geometric” Versus “Arithmetic” Notions.- 8.16. The Arithmetic Criterion for Cyclicity.- 8.17. The “Geometric Artin Conjecture”.- 8.18. Special-values at Positive Integers.- 8.19. The Functional Equation of the Special-values.- 8.20. Applications to Class Groups.- 8.21. The Geometric Criterion for Cyclicity.- 8.22. Magic Numbers.- 8.23. Finiteness in Local and Global Fields.- 8.24. Towards a Theory of the Zeroes.- 8.25. Kapranov’s Higher Dimensional Theory.- 9. ?-functions.- 9.1. Basic Properties of the Carlitz Factorial.- 9.2. Bernoulli-Carlitz Numbers.- 9.3. The ?-ideal.- 9.4. The Arithmetic ?-function.- 9.5. Functional Equations.- 9.6. Finite Interpolations.- 9.7. Another ?-adic ?-function.- 9.8. Gauss Sums.- 9.9. The Geometric ?-function.- 10. Additional Topics.- 10.1. The Geometric Fermat Equation.- 10.2. Geometric Deligne Reciprocity and Solitons.- 10.3. The Tate Conjecture for Drinfeld Modules.- 10.4. Meromorphic Continuations of L-functions.- 10.5. The Structure of the A-module of Rational Points.- 10.6. Log-algebraicity and Special Points.- References.
* A new and fascinating area of math * The author is a fundamental contributor to the field * The first systematic treatment of this subject * Introduces vital areas of current research * Clear exposition, lively style.; The arithmetic of function fields over finite fields is a relatively new area of mathematics. The author has been in the forefront of research in this field since it started and this book is the first systematic treatment of this field. Many applications and open problems are presented and the last section of the book introduces the reader to some of the most vital areas of current research.