Field Arithmetic

Front Matter....Pages I-XVII
Infinite Galois Theory and Profinite Groups....Pages 1-11
Algebraic Function Fields of One Variable....Pages 12-27
The Riemann Hypothesis for Function Fields....Pages 28-42
Plane Curves....Pages 43-53
The Čebotarev Density Theorem....Pages 54-73
Ultraproducts....Pages 74-87
Decision Procedures....Pages 88-100
Algebraically Closed Fields....Pages 101-108
Elements of Algebraic Geometry....Pages 109-128
Pseudo Algebraically Closed Fields....Pages 129-140
Hilbertian Fields....Pages 141-149
The Classical Hilbertian Fields....Pages 150-160
Nonstandard Structures....Pages 161-169
Nonstandard Approach to Hilbert’s Irreducibility Theorem....Pages 170-182
Profinite Groups and Hilbertian Fields....Pages 183-200
The Haar Measure....Pages 201-227
Effective Field Theory and Algebraic Geometry....Pages 228-247
The Elementary Theory of e -free PAC Fields....Pages 248-267
Examples and Applications....Pages 268-285
Projective Groups and Frattini Covers....Pages 286-313
Perfect PAC Fields of Bounded Corank....Pages 314-325
Undecidability....Pages 326-351
Frobenius Fields....Pages 352-367
On ω -free PAC Fields....Pages 368-402
Galois Stratification....Pages 403-421
Galois Stratification over Finite Fields....Pages 422-441
Back Matter....Pages 442-460