Mordell Weil Lattices

Author : Matthias Schütt
Publisher : Springer Nature
ISBN 13 : 9813293012
Total Pages : 431 pages
Book Rating : 4.14/5 ( download)

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Download or read book Mordell–Weil Lattices written by Matthias Schütt and published by Springer Nature. This book was released on 2019-10-17 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Tetsuji Shioda
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.12/5 ( download)

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Download or read book Further Collection: Mordell-Weil Lattices written by Tetsuji Shioda and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Neil Patrick Dummigan
Publisher :
ISBN 13 :
Total Pages : 146 pages
Book Rating : 4.96/5 ( download)

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Download or read book The Second Descent for Certain Families of Mordell-Weil Lattices written by Neil Patrick Dummigan and published by . This book was released on 1993 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Gretchen Rimmasch
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.50/5 ( download)

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Download or read book Lattices and Their Applications to Rational Elliptic Surfaces written by Gretchen Rimmasch and published by . This book was released on 2003 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis discusses some of the invariants of rational elliptic surfaces, namely the Mordell-Weil Group, Mordell-Weil Lattice, and another lattice which will be called the Shioda Lattice. It will begin with a brief overview of rational elliptic surfaces, followed by a discussion of lattices, root systems and Dynkin diagrams. Known results of several authors will then be applied to determine the groups and lattices associated with a given rational elliptic surface, along with a discussion of the uses of these groups and lattices in classifying surfaces.

Author : Jean-P. Serre
Publisher : Springer Science & Business Media
ISBN 13 : 3663106322
Total Pages : 228 pages
Book Rating : 4.26/5 ( download)

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Download or read book Lectures on the Mordell-Weil Theorem written by Jean-P. Serre and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on a course given by J.-P. Serre at the Collège de France in 1980 and 1981. Basic techniques in Diophantine geometry are covered, such as heights, the Mordell-Weil theorem, Siegel's and Baker's theorems, Hilbert's irreducibility theorem, and the large sieve. Included are applications to, for example, Mordell's conjecture, the construction of Galois extensions, and the classical class number 1 problem. Comprehensive bibliographical references.

Author : Klaus Hulek
Publisher : Cambridge University Press
ISBN 13 : 9780521646598
Total Pages : 500 pages
Book Rating : 4.96/5 ( download)

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Download or read book New Trends in Algebraic Geometry written by Klaus Hulek and published by Cambridge University Press. This book was released on 1999-05-13 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing 17 survey and research articles selected from the most outstanding contemporary research topics in algebraic geometry. Several of the articles are expository: among these a beautiful short exposition by Paranjape of the new and very simple approach to the resolution of singularities; a detailed essay by Ito and Nakamura on the ubiquitous A,D,E classification, centred around simple surface singularities; a discussion by Morrison of the new special Lagrangian approach to giving geometric foundations to mirror symmetry; and two deep, informative surveys by Siebert and Behrend on Gromow-Witten invariants treating them from the point of view of algebraic and symplectic geometry. The remaining articles cover a wide cross-section of the most significant research topics in algebraic geometry. This includes Gromow-Witten invariants, Hodge theory, Calabi-Yau 3-folds, mirror symmetry and classification of varieties.

Author : T. Shioda
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.83/5 ( download)

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Download or read book Gröbner Basis, Mordell-Weil Lattices and Deformation of Singularities written by T. Shioda and published by . This book was released on 2009 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Fumio Hazama
Publisher : World Scientific
ISBN 13 : 9814549703
Total Pages : 114 pages
Book Rating : 4.07/5 ( download)

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Download or read book Algebraic Cycles And Related Topics written by Fumio Hazama and published by World Scientific. This book was released on 1995-01-25 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the results of Cleverbio, a project funded by the European Commission. The project examined the process of growth and development of clusters in the biotech industry, identifying and studying the main driving forces. The empirical work involved in-depth analysis of five clusters at different stages of development: Cambridge, the most important cluster in Europe; Heidelberg, one of the strongest in Germany; Aarhus in Denmark; Marseille in France; and Milano in Italy at an early stage of development. Other clusters were also analysed, such as Paris-Evry (France), Uppsala (Sweden), Biovalley (Switzerland), Bay Area and San Diego (US).The ultimate aim of Cleverbio has been to build a normative model that incorporates:• the preconditions for a cluster to grow (scientific base and/or industrial base, innovative financing, etc.);• the driving forces for cluster growth and development, i.e. the key factors of development (new company creation, IP rules, acceptance of biotech products, services and infrastructures, etc.);• best practices in cluster management (barrier removal, network creation, marketing, technology transfer, etc.).The book also identifies different forms of cluster creation. In some cases clusters were born and grew spontaneously as a consequence of the original co-presence of the key success factors (spontaneous clusters); in other cases they were born of the actions of public actors (industry restructuring and industry development policies). Finally, in a few cases, the process of clustering started as a result of a combination of different original conditions (hybrid clusters)./a

Author : John Conway
Publisher : Springer Science & Business Media
ISBN 13 : 1475765681
Total Pages : 778 pages
Book Rating : 4.87/5 ( download)

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Download or read book Sphere Packings, Lattices and Groups written by John Conway and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.

Author : Myung-Hwan Kim
Publisher : American Mathematical Soc.
ISBN 13 : 0821819496
Total Pages : 314 pages
Book Rating : 4.94/5 ( download)

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Download or read book Integral Quadratic Forms and Lattices written by Myung-Hwan Kim and published by American Mathematical Soc.. This book was released on 1999 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of an international conference held at Seoul National University (Korea). Talks covered recent developments in diverse areas related to the theory of integral quadratic forms and hermitian forms, local densities, linear relations and congruences of theta series, zeta functions of prehomogeneous vector spaces, lattices with maximal finite matrix groups, globally irreducible lattices, Mordell-Weil lattices, and more. Articles in the volume represent expository lectures by leading experts on recent developments in the field. The book offers a comprehensive introduction to the current state of knowledge in the arithmetic theory of quadratic forms and provides active directions of research with new results. Topics addressed in the volume emphasize connections with related fields, such as group theory, arithmetic geometry, analytic number theory, and modular forms. The book is an excellent introductory guide for students as well as a rich reference source for researchers.