Theta Invariants Of Euclidean Lattices And Infinite Dimensional Hermitian Vector Bundles Over Arithmetic Curves PDF Download
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Author | : Jean-Benoît Bost |
Publisher | : Springer Nature |
Total Pages | : 365 |
Release | : 2020-08-21 |
Genre | : Mathematics |
ISBN | : 3030443299 |
Download Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves Book in PDF, ePub and Kindle
This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete description of the theta invariants which give rise to a closer parallel with the geometric case. The author then unfolds his theory of infinite Hermitian vector bundles over arithmetic curves and their theta invariants, which provides a conceptual framework to deal with the sequences of lattices occurring in many diophantine constructions. The book contains many interesting original insights and ties to other theories. It is written with extreme care, with a clear and pleasant style, and never sacrifices accessibility to sophistication.
Author | : Emmanuel Peyre |
Publisher | : Springer Nature |
Total Pages | : 469 |
Release | : 2021-03-10 |
Genre | : Mathematics |
ISBN | : 3030575594 |
Download Arakelov Geometry and Diophantine Applications Book in PDF, ePub and Kindle
Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.
Author | : Haruzo Hida |
Publisher | : Springer Science & Business Media |
Total Pages | : 464 |
Release | : 2013-06-13 |
Genre | : Mathematics |
ISBN | : 1461466571 |
Download Elliptic Curves and Arithmetic Invariants Book in PDF, ePub and Kindle
This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics. This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties. Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader. Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory. Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.
Author | : Clay Mathematics Institute. Summer School |
Publisher | : American Mathematical Soc. |
Total Pages | : 396 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780821837153 |
Download Strings and Geometry Book in PDF, ePub and Kindle
Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.
Author | : Matilde Marcolli |
Publisher | : American Mathematical Soc. |
Total Pages | : 152 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821838334 |
Download Arithmetic Noncommutative Geometry Book in PDF, ePub and Kindle
Arithmetic Noncommutative Geometry uses ideas and tools from noncommutative geometry to address questions in a new way and to reinterpret results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at Archimedean places of arithmetic surfaces and varieties. Noncommutative geometry can be expected to say something about topics of arithmetic interest because it provides the right framework for which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry. With a foreword written by Yuri Manin and a brief introduction to noncommutative geometry, this book offers a comprehensive account of the cross fertilization between two important areas, noncommutative geometry and number theory. It is suitable for graduate students and researchers interested in these areas.
Author | : Benson Farb |
Publisher | : American Mathematical Soc. |
Total Pages | : 384 |
Release | : 2006-09-12 |
Genre | : Mathematics |
ISBN | : 0821838385 |
Download Problems on Mapping Class Groups and Related Topics Book in PDF, ePub and Kindle
The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Author | : Steven D. Galbraith |
Publisher | : Cambridge University Press |
Total Pages | : 631 |
Release | : 2012-03-15 |
Genre | : Computers |
ISBN | : 1107013925 |
Download Mathematics of Public Key Cryptography Book in PDF, ePub and Kindle
This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Author | : William A. Stein |
Publisher | : American Mathematical Soc. |
Total Pages | : 290 |
Release | : 2007-02-13 |
Genre | : Mathematics |
ISBN | : 0821839608 |
Download Modular Forms, a Computational Approach Book in PDF, ePub and Kindle
This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
Author | : |
Publisher | : |
Total Pages | : 1380 |
Release | : 1981 |
Genre | : Associations, institutions, etc |
ISBN | : |
Download Associations' Publications in Print Book in PDF, ePub and Kindle
1981- in 2 v.: v.1, Subject index; v.2, Title index, Publisher/title index, Association name index, Acronym index, Key to publishers' and distributors' abbreviations.
Author | : Friedrich Hirzebruch |
Publisher | : Springer |
Total Pages | : 514 |
Release | : 1985 |
Genre | : Electronic books |
ISBN | : |
Download Arbeitstagung Bonn, 1984 Book in PDF, ePub and Kindle