| 书目名称 | Rational Points and Arithmetic of Fundamental Groups | | 副标题 | Evidence for the Sec | | 编辑 | Jakob Stix | | 视频video | | | 概述 | The first exposition of foundational material on the arithmetic of fundamental groups with respect to the Section Conjecture of anabelian Geometry: from the history of the subject to the state of the | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension. | | 出版日期 | Book 2013 | | 关键词 | 14H30,14G05,14H25,11G20,14G32,14F35; ; Anabelian Geometry; Etale Fundamental Group; Rational Points; Sect | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-30674-7 | | isbn_softcover | 978-3-642-30673-0 | | isbn_ebook | 978-3-642-30674-7Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 2013 |
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发表于 2025-3-21 19:43:16
