| 书目名称 | Field Arithmetic | | 编辑 | Michael D. Fried,Moshe Jarden | | 视频video | | | 概述 | Provides a self-contained account of the study of Diophantine fields through their absolute Galois groups.Covers the prerequisites on infinite Galois theory, profinite groups, algebraic function field | | 丛书名称 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati | | 图书封面 |  | | 描述 | .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..Thisfourth 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 conclud | | 出版日期 | Book 2023Latest edition | | 关键词 | Absolute Galois Groups; Algebra; Arithmetic; Counting; Finite Fields; Galois Stratification; Hilbertian Fi | | 版次 | 4 | | doi | https://doi.org/10.1007/978-3-031-28020-7 | | isbn_softcover | 978-3-031-28022-1 | | isbn_ebook | 978-3-031-28020-7Series ISSN 0071-1136 Series E-ISSN 2197-5655 | | issn_series | 0071-1136 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 19:18:36
