Field Arithmetic

Authors:

ISBN: 978-3-540-22811-0 (Print) 978-3-540-26949-6 (Online)

Table of contents (32 chapters)

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  1. Front Matter

    Pages i-xxiii

  2. Chapter

    Pages 1-18

    Infinite Galois Theory and Profinite Groups

  3. Chapter

    Pages 19-51

    Valuations and Linear Disjointness

  4. Chapter

    Pages 52-76

    Algebraic Function Fields of One Variable

  5. Chapter

    Pages 77-94

    The Riemann Hypothesis for Function Fields

  6. Chapter

    Pages 95-106

    Plane Curves

  7. Chapter

    Pages 107-131

    The Chebotarev Density Theorem

  8. Chapter

    Pages 132-148

    Ultraproducts

  9. Chapter

    Pages 149-162

    Decision Procedures

  10. Chapter

    Pages 163-171

    Algebraically Closed Fields

  11. Chapter

    Pages 172-191

    Elements of Algebraic Geometry

  12. Chapter

    Pages 192-217

    Pseudo Algebraically Closed Fields

  13. Chapter

    Pages 218-229

    Hilbertian Fields

  14. Chapter

    Pages 230-265

    The Classical Hilbertian Fields

  15. Chapter

    Pages 266-275

    Nonstandard Structures

  16. Chapter

    Pages 276-289

    Nonstandard Approach to Hilbert’s Irreducibility Theorem

  17. Chapter

    Pages 290-336

    Galois Groups over Hilbertian Fields

  18. Chapter

    Pages 337-361

    Free Profinite Groups

  19. Chapter

    Pages 362-400

    The Haar Measure

  20. Chapter

    Pages 401-426

    Effective Field Theory and Algebraic Geometry

  21. Chapter

    Pages 427-451

    The Elementary Theory of e-Free PAC Fields

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