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Mordell–Weil Lattices

Title
Mordell–Weil Lattices [electronic resource] / by Matthias Schütt, Tetsuji Shioda.
ISBN
9789813293014
Edition
1st ed. 2019.
Publication
Singapore : Springer Singapore : Imprint: Springer, 2019.
Physical Description
1 online resource (XVI, 431 p.) 32 illus., 9 illus. in color.
Local Notes
Access is available to the Yale community.
Access and use
Access restricted by licensing agreement.
Summary
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 with elliptic 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.
Variant and related titles
Springer ENIN.
Other formats
Printed edition:
Printed edition:
Printed edition:
Format
Books / Online
Language
English
Added to Catalog
October 31, 2019
Series
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 70
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 70
Contents
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.
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