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Moduli Spaces Of Abelian Surfaces With Isogeny

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Moduli Spaces Of Abelian Surfaces With Isogeny

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Author : Christina Birkenhake
language : de
Publisher:
Release Date : 1992

Moduli Spaces Of Abelian Surfaces With Isogeny written by Christina Birkenhake and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.

Moduli Of Abelian Varieties

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Author : C. Faber
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-03

Moduli Of Abelian Varieties written by C. Faber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03 with Mathematics categories.

Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics. Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field. The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics.

Moduli Of Supersingular Abelian Varieties

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Author : Ke-Zheng Li
language : en
Publisher: Springer
Release Date : 2006-11-14

Moduli Of Supersingular Abelian Varieties written by Ke-Zheng Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to Äg.g/4Ü, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).

Abelian Varieties

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Author : Wolf P. Barth
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24

Abelian Varieties written by Wolf P. Barth and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Quaternion Algebras

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Author : John Voight
language : en
Publisher: Springer Nature
Release Date : 2021-06-28

Quaternion Algebras written by John Voight and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Mathematics categories.

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.

Complex Abelian Varieties

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Author : Christina Birkenhake
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Complex Abelian Varieties written by Christina Birkenhake and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. ". . . far more readable than most . . . it is also much more complete." Olivier Debarre in Mathematical Reviews, 1994.

Moduli Of Abelian Varieties

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Author : Gerard van der Geer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Moduli Of Abelian Varieties written by Gerard van der Geer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Arithmetic And Geometry Of K3 Surfaces And Calabi Yau Threefolds

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Author : Radu Laza
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-12

Arithmetic And Geometry Of K3 Surfaces And Calabi Yau Threefolds written by Radu Laza and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-12 with Mathematics categories.

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

Riemann And Klein Surfaces Automorphisms Symmetries And Moduli Spaces

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Author : Milagros Izquierdo
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-11-21

Riemann And Klein Surfaces Automorphisms Symmetries And Moduli Spaces written by Milagros Izquierdo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-21 with Mathematics categories.

This volume contains the proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24-28, 2013, at Linköping University. The conference and this volume are devoted to the mathematics that Emilio Bujalance has worked with in the following areas, all with a computational flavor: Riemann and Klein surfaces, automorphisms of real and complex surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties.

Moduli Spaces Of Riemann Surfaces

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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-16

Moduli Spaces Of Riemann Surfaces written by Benson Farb and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 with Mathematics categories.

Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Moduli Spaces Of Abelian Surfaces With Isogeny

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