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The Resource Mordell–Weil Lattices, by Matthias Schütt, Tetsuji Shioda, (electronic resource)

Mordell–Weil Lattices, by Matthias Schütt, Tetsuji Shioda, (electronic resource)

Label
Mordell–Weil Lattices
Title
Mordell–Weil Lattices
Statement of responsibility
by Matthias Schütt, Tetsuji Shioda
Creator
Contributor
Author
Subject
Language
eng
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.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Schütt, Matthias
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Shioda, Tetsuji
Series statement
  • Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,
  • Springer eBooks.
Series volume
70
http://library.link/vocab/subjectName
  • Algebraic geometry
  • Commutative algebra
  • Commutative rings
  • Algebra
  • Field theory (Physics)
  • Category theory (Mathematics)
  • Homological algebra
  • Nonassociative rings
  • Rings (Algebra)
Label
Mordell–Weil Lattices, by Matthias Schütt, Tetsuji Shioda, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-981-32-9301-4
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
978-981-32-9301-4
Dimensions
unknown
Edition
1st ed. 2019.
Extent
1 online resource (XVI, 431 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9789813293014
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
32 illustrations, 9 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1124766850
Label
Mordell–Weil Lattices, by Matthias Schütt, Tetsuji Shioda, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-981-32-9301-4
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
978-981-32-9301-4
Dimensions
unknown
Edition
1st ed. 2019.
Extent
1 online resource (XVI, 431 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9789813293014
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
32 illustrations, 9 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1124766850

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