Mordell-Weil Lattices

• Main Authors: Schütt, Matthias (Author, http://id.loc.gov/vocabulary/relators/aut), Shioda, Tetsuji (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 70
• Subjects: Algebraic geometry.; Commutative algebra.; Commutative rings.; Algebra.; Field theory (Physics).; Category theory (Mathematics).; Homological algebra.; Nonassociative rings.; Rings (Algebra).; Algebraic Geometry.; Commutative Rings and Algebras.; Field Theory and Polynomials.; Category Theory, Homological Algebra.; Non-associative Rings and Algebras.

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...

Table of 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.