| 书目名称 | Field Arithmetic |
| 编辑 | Michael D. Fried,Moshe Jarden |
| 视频video | |
| 概述 | Third revised edition of the classic Ergebnisse volume "Field Arithmetic" by M. Fried and M. Jarden.Improves the second edition in two ways:.1. Removes many typos and mathematical inaccuracies that oc |
| 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 | .Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements...Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of |
| 出版日期 | Book 20083rd edition |
| 关键词 | Absolute Galois Groups; Algebra; Arithmetic; Counting; Finite Fields; Galois Stratification; Hilbertian Fi |
| 版次 | 3 |
| doi | https://doi.org/10.1007/978-3-540-77270-5 |
| isbn_ebook | 978-3-540-77270-5Series ISSN 0071-1136 Series E-ISSN 2197-5655 |
| issn_series | 0071-1136 |
| copyright | Springer-Verlag Berlin Heidelberg 2008 |
发表于 2025-3-21 18:16:10
