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Field Arithmetic /

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This book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois theory, profinite groups, algebraic function fields in one variable and plane curves. It provides complete and eleme...

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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: Cham : Springer Nature Switzerland : Imprint: Springer, 2023.
Edition:4th ed. 2023.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 11
Subjects:
Algebra.
Mathematics.
Algebraic geometry.
Algebraic fields.
Polynomials.
Geometry.
Mathematical logic.
Algebraic Geometry.
Field Theory and Polynomials.
Mathematical Logic and Foundations.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1 Infinite Galois Theory and Profinite Groups
  • 2 Valuations
  • 3 Linear Disjointness
  • 4 Algebraic Function Fields of One Variable
  • 5 The Riemann Hypothesis for Function Fields
  • 6 Plane Curves
  • 7 The Chebotarev Density Theorem
  • 8 Ultraproducts
  • 9 Decision Procedures
  • 10 Algebraically Closed Fields
  • 11 Elements of Algebraic Geometry
  • 12 Pseudo Algebraically Closed Fields
  • 13 Hilbertian Fields
  • 14 The Classical Hilbertian Fields
  • 15 The Diamond Theorem
  • 16 Nonstandard Structures
  • 17 The Nonstandard Approach to Hilbert's Irreducibility Theorem
  • 18 Galois Groups over Hilbertian Fields
  • 19 Small Profinite Groups
  • 20 Free Profinite Groups
  • 21 The Haar Measure
  • 22 Effective Field Theory and Algebraic Geometry
  • 23 The Elementary Theory of ����-Free PAC Fields
  • 24 Problems of Arithmetical Geometry
  • 25 Projective Groups and Frattini Covers
  • 26 PAC Fields and Projective Absolute Galois Groups
  • 27 Frobenius Fields
  • 28 Free Profinite Groups of Infinite Rank
  • 29 Random Elements in Profinite Groups
  • 30 Omega-free PAC Fields
  • 31 Hilbertian Subfields of Galois Extensions
  • 32 Undecidability
  • 33 Algebraically Closed Fields with Distinguished Automorphisms
  • 34 Galois Stratification
  • 35 Galois Stratification over Finite Fields
  • 36 Problems of Field Arithmetic.