Drinfeld Modular Curves
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Drinfeld Modular Curves
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Author : Ernst-Ulrich Gekeler
language : en
Publisher: Springer
Release Date : 2006-11-14
Drinfeld Modular Curves written by Ernst-Ulrich Gekeler 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.
Drinfeld Modules Modular Schemes And Applications
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Author : M Van Der Put
language : en
Publisher: World Scientific
Release Date : 1997-08-27
Drinfeld Modules Modular Schemes And Applications written by M Van Der Put and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-27 with Mathematics categories.
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.
Drinfeld Modules
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Author : Mihran Papikian
language : en
Publisher: Springer Nature
Release Date : 2023-03-31
Drinfeld Modules written by Mihran Papikian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-31 with Mathematics categories.
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.
Optimal Elliptic Curves Discriminants And The Degree Conjecture Over Function Fields
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Author : Mihran Papikian
language : en
Publisher:
Release Date : 2003
Optimal Elliptic Curves Discriminants And The Degree Conjecture Over Function Fields written by Mihran Papikian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Proceedings Of The Workshop On Drinfeld Modules Modular Schemes And Applications
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Author : Ernst-Ulrich Gekeler
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1997
Proceedings Of The Workshop On Drinfeld Modules Modular Schemes And Applications written by Ernst-Ulrich Gekeler and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Heegner Modules And Elliptic Curves
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Author : Martin L. Brown
language : en
Publisher: Springer
Release Date : 2004-08-30
Heegner Modules And Elliptic Curves written by Martin L. Brown and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-30 with Mathematics categories.
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.
Cohomology Of Drinfeld Modular Varieties Part 2 Automorphic Forms Trace Formulas And Langlands Correspondence
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Author :
language : en
Publisher: Cambridge University Press
Release Date :
Cohomology Of Drinfeld Modular Varieties Part 2 Automorphic Forms Trace Formulas And Langlands Correspondence written by and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Compactification Of The Drinfeld Modular Surfaces
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Author : Thomas Lehmkuhl
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Compactification Of The Drinfeld Modular Surfaces written by Thomas Lehmkuhl 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 2000 with categories.
Applications Of Curves Over Finite Fields
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Author : Michael D. Fried
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Applications Of Curves Over Finite Fields written by Michael D. Fried 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 1999 with Mathematics categories.
This volume presents the results of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington (Seattle). The talks were devoted to various aspects of the theory of algebraic curves over finite fields and its numerous applications. The three basic themes are the following: 1. Curves with many rational points. Several articles describe main approaches to the construction of such curves: the Drinfeld modules and fiber product methods, the moduli space approach, and the constructions using classical curves. 2. Monodromy groups of characteristic $p$ covers. A number of authors presented the results and conjectures related to the study of the monodromy groups of curves over finite fields. In particular, they study the monodromy groups from genus 0 covers, reductions of covers, and explicit computation of monodromy groups over finite fields. 3. Zeta functions and trace formulas. To a large extent, papers devoted to this topic reflect the contributions of Professor Bernard Dwork and his students. This conference was the last attended by Professor Dwork before his death, and several papers inspired by his presence include commentaries about the applications of trace formulas and L-function. The volume also contains a detailed introduction paper by Professor Michael Fried, which helps the reader to navigate the material presented in the book.
Many Rational Points
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Author : N.E. Hurt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Many Rational Points written by N.E. Hurt 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 2013-11-11 with Mathematics categories.
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