Field Arithmetic - 9783031280191

Field ArithmeticAuthor(s): Michael D. Fried, Moshe Jarden\nFormat: Hardback\nPublisher: Springer International Publishing AG, Switzerland\nImprint: Springer International Publishing AG\nISBN-13: 9783031280191, 978-3031280191\nSynopsis\nThis 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 undecidab.