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Field arithmetic

Author: Michael D Fried; Moshe Jarden
Publisher: Berlin : Springer, ©2008.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Bd. 11.
Edition/Format:   eBook : Document : English : 3rd ed., rev.View all editions and formats
Summary:

Field Arithmetic explores Diophantine fields through their absolute Galois groups. The treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students  Read more...

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Fried, Michael D., 1942-
Field arithmetic.
Berlin : Springer, ©2008
(OCoLC)232361356
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michael D Fried; Moshe Jarden
ISBN: 9783540772705 3540772707 9783540772699 3540772693
OCLC Number: 233973734
Description: 1 online resource (xxiii, 792 pages) : illustrations.
Contents: 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 theorm --
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 free profinite groups --
Omega-free PAC fields --
Undecidability --
Algebraically closed fields with distinguished automorphisms --
Galois satisfaction --
Galois stratification over finite fields --
Problems of field arithmetic.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Bd. 11.
Responsibility: Michael D. Fried, Moshe Jarden.
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From the reviews of the second edition:"This second and considerably enlarged edition reflects the progress made in field arithmetic during the past two decades. ... The book also contains very Read more...

 
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