Download or read book Drinfeld Modules written by Mihran Papikian and published by Springer Nature. This book was released on 2023-03-31 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory. After the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized. Drinfeld Modules guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic.

Download or read book Drinfeld Modules Modular Schemes And Applications written by M Van Der Put and published by World Scientific. This book was released on 1997-08-27 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his 1974 seminal paper 'Elliptic modules', V G Drinfeld introduced objects into the arithmetic geometry of global function fields which are nowadays known as 'Drinfeld Modules'. They have many beautiful analogies with elliptic curves and abelian varieties. They study of their moduli spaces leads amongst others to explicit class field theory, Jacquet-Langlands theory, and a proof of the Shimura-Taniyama-Weil conjecture for global function fields.This book constitutes a carefully written instructional course of 12 lectures on these subjects, including many recent novel insights and examples. The instructional part is complemented by research papers centering around class field theory, modular forms and Heegner points in the theory of global function fields.The book will be indispensable for everyone who wants a clear view of Drinfeld's original work, and wants to be informed about the present state of research in the theory of arithmetic geometry over function fields.

Download or read book Drinfeld Modular Curves written by Ernst-Ulrich Gekeler and published by Springer. This book was released on 2006-11-14 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Compactification of the Drinfeld Modular Surfaces written by Thomas Lehmkuhl and published by American Mathematical Soc.. This book was released on 2009-01-21 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article the author describes in detail a compactification of the moduli schemes representing Drinfeld modules of rank 2 endowed with some level structure. The boundary is a union of copies of moduli schemes for Drinfeld modules of rank 1, and its points are interpreted as Tate data. The author also studies infinitesimal deformations of Drinfeld modules with level structure.

Download or read book Many Rational Points written by N.E. Hurt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators." "The book will be of use to mathematicians, physicists and engineers interested in the mathematical methods of algebraic geometry as they apply to coding theory and cryptography."--Jacket

Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1992-06 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Cohomology of Drinfeld Modular Varieties Part 1 Geometry Counting of Points and Local Harmonic Analysis written by Gérard Laumon and published by Cambridge University Press. This book was released on 1996 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. The present volume is devoted to the geometry of these varieties, and to the local harmonic analysis needed to compute their cohomology. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated.

Download or read book Heegner Modules and Elliptic Curves written by and published by Springer Science & Business Media. This book was released on 2004 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Arithmetic of Drinfeld Modules written by Dragos Florin Ghioca and published by . This book was released on 2005 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Mordell Weil Theorem Rigidity and Pairings for Drinfeld Modules written by Bjorn Poonen and published by . This book was released on 1994 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Noncommutative Geometry and Number Theory written by Caterina Consani and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1992-06 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Crossed Modules written by Friedrich Wagemann and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-10-25 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents material in two parts. Part one provides an introduction to crossed modules of groups, Lie algebras and associative algebras with fully written out proofs and is suitable for graduate students interested in homological algebra. In part two, more advanced and less standard topics such as crossed modules of Hopf algebra, Lie groups, and racks are discussed as well as recent developments and research on crossed modules.

Download or read book 75 Years of Mathematics of Computation written by Susanne C. Brenner and published by American Mathematical Soc.. This book was released on 2020-07-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions. On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.

Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.

Download or read book Hopf Algebras in Noncommutative Geometry and Physics written by Stefaan Caenepeel and published by CRC Press. This book was released on 2019-05-07 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the

Download or read book Basic Structures of Function Field Arithmetic written by David Goss and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062