LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	512
Title	Field Arithmetic (EBook /) / by Michael D. Fried, Moshe Jarden.
Author	Fried, Michael D.
Added Personal Name	Jarden, Moshe
Other name(s)	SpringerLink (Online service)
Edition statement	4th ed. 2023.
Publication	Cham : : Springer Nature Switzerland : : Imprint: Springer, , 2023.
Physical Details	XXXI, 827 p. : online resource.
Series	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 2197-5655 ; ; 11
ISBN	9783031280207
Summary Note	This book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois theory, profinite groups, algebraic function fields in one variable and plane curves. It provides complete and elementary proofs of the Chebotarev density theorem and the Riemann hypothesis for function fields, together with material on ultraproducts, decision procedures, the elementary theory of algebraically closed fields, undecidability and nonstandard model theory, including a nonstandard proof of Hilbert's irreducibility theorem. The focus then turns to the study of pseudo algebraically closed (PAC) fields, related structures and associated decidability and undecidability results. PAC fields (fields K with the property that every absolutely irreducible variety over K has a rational point) first arose in the elementary theory of finite fields and have deep connections with number theory. This fourth edition substantially extends, updates and clarifies the previous editions of this celebrated book, and includes a new chapter on Hilbertian subfields of Galois extensions. Almost every chapter concludes with a set of exercises and bibliographical notes. An appendix presents a selection of open research problems. Drawing from a wide literature at the interface of logic and arithmetic, this detailed and self-contained text can serve both as a textbook for graduate courses and as an invaluable reference for seasoned researchers.:
Contents note	1 Infinite Galois Theory and Profinite Groups -- 2 Valuations -- 3 Linear Disjointness -- 4 Algebraic Function Fields of One Variable -- 5 The Riemann Hypothesis for Function Fields -- 6 Plane Curves -- 7 The Chebotarev Density Theorem -- 8 Ultraproducts -- 9 Decision Procedures -- 10 Algebraically Closed Fields -- 11 Elements of Algebraic Geometry -- 12 Pseudo Algebraically Closed Fields -- 13 Hilbertian Fields -- 14 The Classical Hilbertian Fields -- 15 The Diamond Theorem -- 16 Nonstandard Structures -- 17 The Nonstandard Approach to Hilbert’s Irreducibility Theorem -- 18 Galois Groups over Hilbertian Fields -- 19 Small Profinite Groups -- 20 Free Profinite Groups -- 21 The Haar Measure -- 22 Effective Field Theory and Algebraic Geometry -- 23 The Elementary Theory of ��-Free PAC Fields -- 24 Problems of Arithmetical Geometry -- 25 Projective Groups and Frattini Covers -- 26 PAC Fields and Projective Absolute Galois Groups -- 27 Frobenius Fields -- 28 Free Profinite Groups of Infinite Rank -- 29 Random Elements in Profinite Groups -- 30 Omega-free PAC Fields -- 31 Hilbertian Subfields of Galois Extensions -- 32 Undecidability -- 33 Algebraically Closed Fields with Distinguished Automorphisms -- 34 Galois Stratification -- 35 Galois Stratification over Finite Fields -- 36 Problems of Field Arithmetic.
Mode of acces to digital resource	Digital reproduction.-
	Cham :
	Springer International Publishing,
	2023. -
	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-031-28020-7
Links to Related Works	Subject References: Algebra . Algebraic fields . Algebraic Geometry . Field Theory and Polynomials . Geometry . Mathematical logic . Mathematical Logic and Foundations . Mathematics . Polynomials . Authors: author . Fried, Michael D. . Jarden, Moshe . Corporate Authors: SpringerLink (Online service) . Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics . Classification: 512 .

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Field Arithmetic

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