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| Author | : Mihran Papikian |
| Publisher | : Springer Nature |
| Total Pages | : 541 |
| Release | : 2023-03-31 |
| Genre | : Mathematics |
| ISBN | : 3031197070 |
Download Drinfeld Modules Book in PDF, ePub and Kindle
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.
| Author | : M Van Der Put |
| Publisher | : World Scientific |
| Total Pages | : 378 |
| Release | : 1997-08-27 |
| Genre | : Mathematics |
| ISBN | : 9814546402 |
Download Drinfeld Modules, Modular Schemes And Applications Book in PDF, ePub and Kindle
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.
| Author | : Ernst-Ulrich Gekeler |
| Publisher | : Springer |
| Total Pages | : 122 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540473866 |
Download Drinfeld Modular Curves Book in PDF, ePub and Kindle
| Author | : Gérard Laumon |
| Publisher | : Cambridge University Press |
| Total Pages | : 362 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0521470609 |
Download Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis Book in PDF, ePub and Kindle
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.
| Author | : Thomas Lehmkuhl |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 113 |
| Release | : 2009-01-21 |
| Genre | : Science |
| ISBN | : 0821842447 |
Download Compactification of the Drinfeld Modular Surfaces Book in PDF, ePub and Kindle
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.
| Author | : Yuval Z Flicker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 150 |
| Release | : 2013-01-04 |
| Genre | : Mathematics |
| ISBN | : 1461458889 |
Download Drinfeld Moduli Schemes and Automorphic Forms Book in PDF, ePub and Kindle
Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author’s original work establishing the correspondence between ell-adic rank r Galois representations and automorphic representations of GL(r) over a function field, in the local case, and, in the global case, under a restriction at a single place. It develops Drinfeld’s theory of elliptic modules, their moduli schemes and covering schemes, the simple trace formula, the fixed point formula, as well as the congruence relations and a "simple" converse theorem, not yet published anywhere. This version, based on a recent course taught by the author at The Ohio State University, is updated with references to research that has extended and developed the original work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as a valuable resource to facilitate an entrance to this fascinating area of mathematics.
| Author | : Dragos Florin Ghioca |
| Publisher | : |
| Total Pages | : 340 |
| Release | : 2005 |
| Genre | : |
| ISBN | : |
Download The Arithmetic of Drinfeld Modules Book in PDF, ePub and Kindle
| Author | : Martin L. Brown |
| Publisher | : Springer |
| Total Pages | : 523 |
| Release | : 2004-08-30 |
| Genre | : Mathematics |
| ISBN | : 3540444750 |
Download Heegner Modules and Elliptic Curves Book in PDF, ePub and Kindle
Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the cohomology of the Heegner module is the main technical result and is applied to prove the Tate conjecture for a class of elliptic surfaces over finite fields, this conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.
| Author | : Arkady. Berenstein |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 265 |
| Release | : 2013-05-01 |
| Genre | : Mathematics |
| ISBN | : 082188980X |
Download Noncommutative Birational Geometry, Representations and Combinatorics Book in PDF, ePub and Kindle
"This volume contains the proceedings of the AMS Special Session on Noncommutative Birational Geometry, Representations and Cluster Algebras, held from January 6-7, 2012, in Boston, MA. The papers deal with various aspects of noncommutative birational geometry and related topics, focusing mainly on structure and representations of quantum groups and algebras, braided algebras, rational series in free groups, Poisson brackets on free algebras, and related problems in combinatorics. This volume is useful for researchers and graduate students in mathematics and mathematical physics who want to be introduced to different areas of current research in the new area of noncommutative algebra and geometry."--Publisher's website.
| Author | : S.D. Adhikari |
| Publisher | : Springer |
| Total Pages | : 280 |
| Release | : 2002-01-01 |
| Genre | : Mathematics |
| ISBN | : 9386279096 |
Download Current Trends in Number Theory Book in PDF, ePub and Kindle
Proceedings of the International Conference on Number Theory, held at Allahabad in November 2000.
