<電子ブック>
Mordell–Weil Lattices / by Matthias Schütt, Tetsuji Shioda
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 70)
版 | 1st ed. 2019. |
---|---|
出版者 | (Singapore : Springer Nature Singapore : Imprint: Springer) |
出版年 | 2019 |
本文言語 | 英語 |
大きさ | XVI, 431 p. 32 illus., 9 illus. in color : online resource |
著者標目 | *Schütt, Matthias author Shioda, Tetsuji author SpringerLink (Online service) |
件 名 | LCSH:Algebraic geometry LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic fields LCSH:Polynomials LCSH:Algebra, Homological LCSH:Nonassociative rings FREE:Algebraic Geometry FREE:Commutative Rings and Algebras FREE:Field Theory and Polynomials FREE:Category Theory, Homological Algebra FREE:Non-associative Rings and Algebras |
一般注記 | Introduction -- Lattices -- Elliptic Curves -- Algebraic surfaces -- Elliptic surfaces -- Mordell--Weil Lattices -- Rational Elliptic Surfaces -- Rational elliptic surfaces and E8-hierarchy -- Galois Representations and Algebraic Equations -- Elliptic K3 surfaces 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 E6, E7 and E8. 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 the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory HTTP:URL=https://doi.org/10.1007/978-981-32-9301-4 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9789813293014 |
|
電子リソース |
|
EB00228554 |
類似資料
この資料の利用統計
このページへのアクセス回数:1回
※2017年9月4日以降