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Field Arithmetic

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Cover of 'Field Arithmetic'

Table of Contents

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    Book Overview
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    Chapter 1 Infinite Galois Theory and Profinite Groups
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    Chapter 2 Valuations
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    Chapter 3 Linear Disjointness
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    Chapter 4 Algebraic Function Fields of One Variable
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    Chapter 5 The Riemann Hypothesis for Function Fields
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    Chapter 6 Plane Curves
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    Chapter 7 The Chebotarev Density Theorem
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    Chapter 8 Ultraproducts
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    Chapter 9 Decision Procedures
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    Chapter 10 Algebraically Closed Fields
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    Chapter 11 Elements of Algebraic Geometry
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    Chapter 12 Pseudo Algebraically Closed Fields
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    Chapter 13 Hilbertian Fields
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    Chapter 14 The Classical Hilbertian Fields
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    Chapter 16 Nonstandard Structures
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    Chapter 17 The Nonstandard Approach to Hilbert’s Irreducibility Theorem
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    Chapter 18 Galois Groups over Hilbertian Fields
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    Chapter 19 Small Profinite Groups
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    Chapter 20 Free Profinite Groups
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    Chapter 21 The Haar Measure
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    Chapter 22 Effective Field Theory and Algebraic Geometry
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    Chapter 23 The Elementary Theory of 𝒆-Free PAC Fields
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    Chapter 25 Projective Groups and Frattini Covers
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    Chapter 26 PAC Fields and Projective Absolute Galois Groups
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    Chapter 27 Frobenius Fields
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    Chapter 28 Free Profinite Groups of Infinite Rank
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    Chapter 29 Random Elements in Profinite Groups
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    Chapter 30 Omega-free PAC Fields
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    Chapter 31 Hilbertian Subfields of Galois Extensions
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    Chapter 32 Undecidability
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    Chapter 33 Algebraically Closed Fields with Distinguished Automorphisms
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    Chapter 34 Galois Stratification
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    Chapter 35 Galois Stratification over Finite Fields
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    Chapter 36 Problems of Field Arithmetic
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Title
Field Arithmetic
Published by
Springer Nature Switzerland, May 2023
DOI 10.1007/978-3-031-28020-7
ISBNs
978-3-03-128019-1, 978-3-03-128020-7
Authors

Fried, Michael D., Jarden, Moshe

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