內容簡介

To those precious colleagues who can appreciate the goals of and connections to other aresa .To those who acknowledge the depth of what we already know from the absorbed contribution of previous generations before we address our papers.To those can transcend the hubris of today’s mathematical community.

目錄

Table of Contents

Chapter 1.Infinite Galois Theory and Profinite Groups

Chapter 2.Valuations and Linear Disjointness

Chapter 3.Algebraic Function Fields of One Variable

Chapter 4.The Riemann Hypothesis for Function Fields

Chapter 5.Plane Curves

Chapter 6.The Chebotarev Density Theorem

Chapter 7.Ultraproducts

Chapter 8.Decision Procedures

Chapter 9.Algebraically Closed Fields

Chapter 10.Elements of Algebraic Geometry

Chapter 11.Pseudo Algebraically Closed Fields

Chapter 12.Hilbertian Fields

Chapter 13.The Classical Hilbertian Fields

Chapter 14.Nonstandard Structures

Chapter 15.Nonstandard Approach to Hilbert’s Irreducibility Theorem

Chapter 16.Galois Groups over Hilbertian Fields

Chapter 17.Free Profinite Groups

Chapter 18.The Haar Measure

Chapter 19.Effective Field Theory and Algebraic Geometry

Chapter 20.The Elementary Theory of e-Free PAC Fields

Chapter 21.Problems of Arithmetical Geometry

Chapter 22.Projective Groups and Frattini Covers

Chapter 23.PAC Fields and Projective Absolute Galois Groups

Chapter 24.Frobenius Fields

Chapter 25.Free Profinite Groups of Infinite Rank

Chapter 26.Random Elements in Free Profinite Groups

Chapter 27.Omega-Free PAC Fields

Chapter 28.Undecidability

Chapter 29.Algebraically Closed Fields with Distinguished Automorphisms

Chapter 30.Galois Stratification

Chapter 31.Galois Stratification over Finite Fields

Chapter 32.Problems of Field Arithmetic

Table of Contents

References

Index