東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Mordell-Weil lattices

Schutt, Matthias.

Linked to FindBook

Google Book

Amazon

博客來

Mordell-Weil lattices

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mordell-Weil lattices/ by Matthias Schutt, Tetsuji Shioda.
Author:	Schutt, Matthias.
other author:	Shioda, Tetsuji.
Published:	Singapore :Springer Singapore : : 2019.,
Description:	xvi, 431 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Lattice theory. -
Online resource:	https://doi.org/10.1007/978-981-32-9301-4
ISBN:	9789813293014

Mordell-Weil lattices
Schutt, Matthias.

Mordell-Weil lattices[electronic resource] /by Matthias Schutt, Tetsuji Shioda. - Singapore :Springer Singapore :2019. - xvi, 431 p. :ill. (some col.), digital ;24 cm. - Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics,v.700071-1136 ;. - Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics ;v.70..

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 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.

ISBN: 9789813293014

Standard No.: 10.1007/978-981-32-9301-4doiSubjects--Topical Terms:

532024
Lattice theory.

LC Class. No.: QA171.5 / .S386 2019

Dewey Class. No.: 511.33

Mordell-Weil lattices
LDR:02791nmm a2200337 a 4500 001 2219063
003 DE-He213
005 20200130164943.0
006 m d
007 cr nn 008maaau
008 201126s2019 si s 0 eng d
020 $a 9789813293014 $q (electronic bk.)
020 $a 9789813293007 $q (paper)
024 7 $a 10.1007/978-981-32-9301-4 $2 doi
035 $a 978-981-32-9301-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA171.5 $b .S386 2019
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 511.33 $2 23
090 $a QA171.5 $b .S396 2019
100 1 $a Schutt, Matthias. $3 2108879
245 1 0 $a Mordell-Weil lattices $h [electronic resource] / $c by Matthias Schutt, Tetsuji Shioda.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2019.
300 $a xvi, 431 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics, $x 0071-1136 ; $v v.70
505 0 $a 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.
520 $a 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.
650 0 $a Lattice theory. $3 532024
650 1 4 $a Algebraic Geometry. $3 893861
650 2 4 $a Commutative Rings and Algebras. $3 891076
650 2 4 $a Field Theory and Polynomials. $3 891077
650 2 4 $a Category Theory, Homological Algebra. $3 899944
650 2 4 $a Non-associative Rings and Algebras. $3 891108
700 1 $a Shioda, Tetsuji. $3 3454031
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Ergebnisse der mathematik und ihrer grenzgebiete. 3. folge / a series of modern surveys in mathematics ; $v v.70. $3 3454032
856 4 0 $u https://doi.org/10.1007/978-981-32-9301-4
950 $a Mathematics and Statistics (Springer-11649)