【目 录】
Chapter 1 Infinite Galois Theory and Profinite Groups//1
Chapter 2 Valuations and Linear Disjointness//19
Chapter 3 Algebraic Function Fields of One Variable//52
Chapter 4 The Riemann Hypothesis for Function Fields//77
Chapter 5 Plane Curves//95
Chapter 6 The Chebotarev Density Theorem//107
Chapter 7 Ultraproducts//132
Chapter 8 Decision Procedures//149
Chapter 9 Algebraically Closed Fields//163
Chapter 10 Elements of Algebraic Geometry//172
Chapter 11 Pseudo Algebraically Closed Fields//192
Chapter 12 Hilbertian Fields//219
Chapter 13 The Classical Hilbertian Fields//231
Chapter 14 Nonstandard Structures//267
Chapter 15 Nonstandard Approach to Hilbert’s Irreducibility Theorem//277
Chapter 16 Galois Groups over Hilbertian Fields//291
Chapter 17 Free Profinite Groups//338
Chapter 18 The Haar Measure//363
Chapter 19 Effective Field Theory and Algebraic Geometry//403
Chapter 20 The Elementary Theory of e-Free PAC Fields//429
Chapter 21 Problems of Arithmetical Geomentry//454
Chapter 22 Projective Groups and Frattini Covers//497
Chapter 23 PAC Fields and Projective Absolute Galois Groups//544
Chapter 24 Frobenius Fields//562
Chapter 25 Free Profinite Groups of Infinite Rank//594
Chapter 26 Random Elements in Free Profinite Groups//635
Chapter 27 Omega-Free PAC Fields//655
Chapter 28 Undecidability//671
Chapter 29 Algebraically Closed Fields with Distinguished Automorphisms//698
Chapter 30 Galois Stratification//708
Chapter 31 Galois Stratification over Finite Fields//730
Chapter 32 Problems of Fields Arithmetic//751
References//761
Index//780
