| 书目名称 | Mordell–Weil Lattices | | 编辑 | Matthias Schütt,Tetsuji Shioda | | 视频video | | | 概述 | Is the first comprehensive introduction of Mordell–Weil lattices that does not assume extensive prerequisites.Shows that the theory of Mordell–Weil lattices itself is very powerful yet relatively easy | | 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 lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics..The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of .E.6., .E.7. and .E.8.. They also explain a connection to the classical topic of the 27 lines on a cubic surface..Two chapters deal withelliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present th | | 出版日期 | Book 2019 | | 关键词 | Mordell--Weil lattice; lattices and sphere packings; elliptic curves and surfaces; K3 surface; Galois re | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-32-9301-4 | | isbn_softcover | 978-981-32-9303-8 | | isbn_ebook | 978-981-32-9301-4Series ISSN 0071-1136 Series E-ISSN 2197-5655 | | issn_series | 0071-1136 | | copyright | Springer Nature Singapore Pte Ltd. 2019 |
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发表于 2025-3-21 19:16:29
