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001469851 001__ 1469851
001469851 003__ OCoLC
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001469851 019__ $$a1382525255$$a1382694242
001469851 020__ $$a9783031280207$$q(electronic bk.)
001469851 020__ $$a3031280202$$q(electronic bk.)
001469851 020__ $$z9783031280191
001469851 020__ $$z3031280199
001469851 0247_ $$a10.1007/978-3-031-28020-7$$2doi
001469851 035__ $$aSP(OCoLC)1384442353
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001469851 1001_ $$aFried, Michael D.,$$d1942-$$eauthor.
001469851 24510 $$aField arithmetic /$$cMichael D. Fried, Moshe Jarden.
001469851 250__ $$aFourth edition.
001469851 264_1 $$aCham :$$bSpringer,$$c[2023]
001469851 264_4 $$c©2023
001469851 300__ $$a1 online resource (xxxi, 827 pages).
001469851 336__ $$atext$$btxt$$2rdacontent
001469851 337__ $$acomputer$$bc$$2rdamedia
001469851 338__ $$aonline resource$$bcr$$2rdacarrier
001469851 4901_ $$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics,$$x2197-5655 ;$$vvolume 11
001469851 504__ $$aIncludes bibliographical references and index.
001469851 5050_ $$a1 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 Hilbert⁰́b9s 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 ¿̐ư¿̐ư¿̐ư¿̐ư-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.
001469851 506__ $$aAccess limited to authorized users.
001469851 520__ $$aThis 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.
001469851 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed June 21, 2023).
001469851 650_0 $$aAlgebraic fields.
001469851 650_0 $$aAlgebraic number theory.
001469851 655_0 $$aElectronic books.
001469851 7001_ $$aJarden, Moshe,$$d1942-$$eauthor.
001469851 77608 $$iPrint version:$$aFried, Michael D.$$tField Arithmetic$$dCham : Springer,c2023$$z9783031280191
001469851 830_0 $$aErgebnisse der Mathematik und ihrer Grenzgebiete ;$$v3. Folge, Bd. 11.$$x2197-5655
001469851 852__ $$bebk
001469851 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-28020-7$$zOnline Access$$91397441.1
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