Field Arithmetic

Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar mea...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Fried, Michael D. (Συγγραφέας), Jarden, Moshe (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
Έκδοση:Third Edition.
Σειρά:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 11
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • Infinite Galois Theory and Profinite Groups
  • Valuations and Linear Disjointness
  • Algebraic Function Fields of One Variable
  • The Riemann Hypothesis for Function Fields
  • Plane Curves
  • The Chebotarev Density Theorem
  • Ultraproducts
  • Decision Procedures
  • Algebraically Closed Fields
  • Elements of Algebraic Geometry
  • Pseudo Algebraically Closed Fields
  • Hilbertian Fields
  • The Classical Hilbertian Fields
  • Nonstandard Structures
  • Nonstandard Approach to Hilbert’s Irreducibility Theorem
  • Galois Groups over Hilbertian Fields
  • Free Profinite Groups
  • The Haar Measure
  • Effective Field Theory and Algebraic Geometry
  • The Elementary Theory of e-Free PAC Fields
  • Problems of Arithmetical Geometry
  • Projective Groups and Frattini Covers
  • PAC Fields and Projective Absolute Galois Groups
  • Frobenius Fields
  • Free Profinite Groups of Infinite Rank
  • Random Elements in Profinite Groups
  • Omega-Free PAC Fields
  • Undecidability
  • Algebraically Closed Fields with Distinguished Automorphisms
  • Galois Stratification
  • Galois Stratification over Finite Fields
  • Problems of Field Arithmetic.