Field arithmetic.(3rd ed., rev.)

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 -- Ele...

Full description

Saved in:
Bibliographic Details
Main Authors: Fried, Michael D., Jarden, Moshe
Format: Book
Language:English
Published: Springer 2017
Subjects:
Online Access:http://repository.vnu.edu.vn/handle/VNU_123/31732
http://dx.doi.org/10.1007/978-3-540-77270-5
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Vietnam National University, Hanoi
Language: English
Description
Summary: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