Drinfeld Modules Modular Schemes And Applications
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| Author | : M Van Der Put |
| Publisher | : World Scientific |
| Total Pages | : 378 |
| Release | : 1997-08-27 |
| Genre | : Mathematics |
| ISBN | : 9814546402 |
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 | : World Scientific Publishing Company Incorporated |
| Total Pages | : 361 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9789810230678 |
| Author | : E.-U. Gekeler |
| Publisher | : |
| Total Pages | : 361 |
| Release | : 1997 |
| Genre | : |
| ISBN | : |
| Author | : Ernst-Ulrich Gekeler |
| Publisher | : Springer |
| Total Pages | : 122 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540473866 |
| Author | : Yuval Z Flicker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 150 |
| Release | : 2013-01-04 |
| Genre | : Mathematics |
| ISBN | : 1461458889 |
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 | : Jean Fresnel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 303 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461200415 |
Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.
| Author | : Chris Christensen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 778 |
| Release | : 2011-06-27 |
| Genre | : Mathematics |
| ISBN | : 3642184871 |
Proceedings of the Conference on Algebra and Algebraic Geometry with Applications, July 19 – 26, 2000, at Purdue University to honor Professor Shreeram S. Abhyankar on the occasion of his seventieth birthday. Eighty-five of Professor Abhyankar's students, collaborators, and colleagues were invited participants. Sixty participants presented papers related to Professor Abhyankar's broad areas of mathematical interest. Sessions were held on algebraic geometry, singularities, group theory, Galois theory, combinatorics, Drinfield modules, affine geometry, and the Jacobian problem. This volume offers an outstanding collection of papers by expert authors.
| Author | : David Goss |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642614809 |
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
| Author | : Mihran Papikian |
| Publisher | : Springer Nature |
| Total Pages | : 541 |
| Release | : 2023-03-31 |
| Genre | : Mathematics |
| ISBN | : 3031197070 |
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 | : Thomas Lehmkuhl |
| Publisher | : American Mathematical Society(RI) |
| Total Pages | : 113 |
| Release | : 2014-09-11 |
| Genre | : MATHEMATICS |
| ISBN | : 9781470405274 |
The author describes a compactification of the moduli schemes representing Drinfeld modules of rank 2 endowed with some level structure. He also studies infinitesimal deformations of Drinfeld modules with level structure.
