@article{1469851,
      recid = {1469851},
      author = {Fried, Michael D., and Jarden, Moshe,},
      title = {Field arithmetic /},
      pages = {1 online resource (xxxi, 827 pages).},
      abstract = {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.},
      url = {http://library.usi.edu/record/1469851},
      doi = {https://doi.org/10.1007/978-3-031-28020-7},
}