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Mordell–Weil Lattices

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Mordell–Weil Lattices

Matthias Schütt, Tetsuji Shioda

Springer
Collection: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati
Publication date : 2019-10-17

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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.

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About the book

Author

Matthias Schütt , Tetsuji Shioda

Imprint

Springer

Collection

Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati

Publication date

2019-10-17

Pages

431 pages

Print ISBN

9789813293007

Language

English

Ebook informations

EAN PDF

9789813293014

Price

£119.50

Copy count 4

Print count 43

File size 7127 Ko

Informations accessibility

EAN EPUB

9789813293014

Price

£119.50

Copy count 4

Print count 43

File size 28314 Ko

Informations accessibility

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About author(s)

Matthias Schütt

Tetsuji Shioda

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