The Resource Mordell–Weil Lattices, by Matthias Schütt, Tetsuji Shioda, (electronic resource)
Mordell–Weil Lattices, by Matthias Schütt, Tetsuji Shioda, (electronic resource)
Resource Information
The item Mordell–Weil Lattices, by Matthias Schütt, Tetsuji Shioda, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Mordell–Weil Lattices, by Matthias Schütt, Tetsuji Shioda, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 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.
 Language
 eng
 Edition
 1st ed. 2019.
 Extent
 1 online resource (XVI, 431 pages)
 Contents

 Introduction
 Lattices
 Elliptic Curves
 Algebraic surfaces
 Elliptic surfaces
 MordellWeil Lattices
 Rational Elliptic Surfaces
 Rational elliptic surfaces and E8hierarchy
 Galois Representations and Algebraic Equations
 Elliptic K3 surfaces
 Isbn
 9789813293014
 Label
 Mordell–Weil Lattices
 Title
 Mordell–Weil Lattices
 Statement of responsibility
 by Matthias Schütt, Tetsuji Shioda
 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.
 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)
 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  MordellWeil Lattices  Rational Elliptic Surfaces  Rational elliptic surfaces and E8hierarchy  Galois Representations and Algebraic Equations  Elliptic K3 surfaces
 Control code
 9789813293014
 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, noncommercial 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)
 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  MordellWeil Lattices  Rational Elliptic Surfaces  Rational elliptic surfaces and E8hierarchy  Galois Representations and Algebraic Equations  Elliptic K3 surfaces
 Control code
 9789813293014
 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, noncommercial 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/Mordell%E2%80%93WeilLatticesbyMatthiasSch%C3%BCtt/E55mHtfMrd8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/Mordell%E2%80%93WeilLatticesbyMatthiasSch%C3%BCtt/E55mHtfMrd8/">Mordell–Weil Lattices, by Matthias Schütt, Tetsuji Shioda, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>