Field Arithmetic

Field Arithmetic by Michael D. Fried, Moshe Jarden.

Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar mea...

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Bibliographic Details
Main Authors: Fried, Michael D. (Author), Jarden, Moshe (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1986.
Edition:1st ed. 1986.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 11
Springer eBook Collection.
Subjects:
Algebra.
Field theory (Physics).
Mathematical logic.
Algebraic geometry.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1. Infinite Galois Theory and Profinite Groups
  • 2. Algebraic Function Fields of One Variable
  • 3. The Riemann Hypothesis for Function Fields
  • 4. Plane Curves
  • 5. The ?ebotarev Density Theorem
  • 6. Ultraproducts
  • 7. Decision Procedures
  • 8. Algebraically Closed Fields
  • 9. Elements of Algebraic Geometry
  • 10. Pseudo Algebraically Closed Fields
  • 11. Hilbertian Fields
  • 12. The Classical Hilbertian Fields
  • 13. Nonstandard Structures
  • 14. Nonstandard Approach to Hilbert’s Irreducibility Theorem
  • 15. Profinite Groups and Hilbertian Fields
  • 16. The Haar Measure
  • 17. Effective Field Theory and Algebraic Geometry
  • 18. The Elementary Theory of e-free PAC Fields
  • 19. Examples and Applications
  • 20. Projective Groups and Frattini Covers
  • 21. Perfect PAC Fields of Bounded Corank
  • 22. Undecidability
  • 23. Frobenius Fields
  • 24. On ?-free PAC Fields
  • 25. Galois Stratification
  • 26. Galois Stratification over Finite Fields
  • Open Problems
  • References.

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