Rigid Local Systems
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Rigid Local Systems
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Rigid Local Systems written by Nicholas M. Katz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1,infinity}. His investigation was successful, largely because any such (irreducible) local system is rigid in the sense that it is globally determined as soon as one knows separately each of its local monodromies. It became clear that luck played a role in Riemann's success: most local systems are not rigid. Yet many classical functions are solutions of differential equations whose local systems are rigid, including both of the standard nth order generalizations of the hypergeometric function, n F n-1's, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P1-{a finite set of points} and recognizing which collections of independently given local monodromies arise as the local monodromies of irreducible rigid local systems. Although the problems addressed here go back to Riemann, and seem to be problems in complex analysis, their solutions depend essentially on a great deal of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne's proof of his far-reaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the l-adic Fourier Transform.
Local Systems In Algebraic Arithmetic Geometry
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Author : Hélène Esnault
language : en
Publisher: Springer Nature
Release Date : 2023-09-19
Local Systems In Algebraic Arithmetic Geometry written by Hélène Esnault and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-19 with Mathematics categories.
The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci. This monograph provides a unique compelling and concise overview of an active area of research and is useful to students looking to get into this area. It is of interest to a wide range of researchers and is a useful reference for newcomers and experts alike.
Nonholonomic Motion Of Rigid Mechanical Systems From A Dae Viewpoint
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Author : Patrick J. Rabier
language : en
Publisher: SIAM
Release Date : 2000-01-01
Nonholonomic Motion Of Rigid Mechanical Systems From A Dae Viewpoint written by Patrick J. Rabier and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
Focuses on rigid body systems subjected to kinematic constraints and discusses in detail how the equations of motion are developed. The authors show that such motions can be modeled in terms of differential algebraic equations (DAEs), provided only that the correct variables are introduced.
Lectures On Formal And Rigid Geometry
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Author : Siegfried Bosch
language : en
Publisher: Springer
Release Date : 2014-08-22
Lectures On Formal And Rigid Geometry written by Siegfried Bosch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Mathematics categories.
The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Recent Advances In Hodge Theory
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Author : Matt Kerr
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-04
Recent Advances In Hodge Theory written by Matt Kerr 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 2016-02-04 with Mathematics categories.
Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2008
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures
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Author : Rajendra Bhatia
language : en
Publisher: World Scientific
Release Date : 2011-06-06
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures written by Rajendra Bhatia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Dynamics And Control Of Electrical Drives
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Author : Wach Piotr
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-28
Dynamics And Control Of Electrical Drives written by Wach Piotr 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 2011-04-28 with Technology & Engineering categories.
Dynamics is a science concerned with movement and changes. In the most general approach it relates to life processes as well as behavior in nature in rest. It governs small particles, technical objects, conversion of matter and materials but also concerns people, groups of people in their individual and, in particular, social dimension. In dynamics we always have to do with causes or stimuli for motion, the rules of reaction or behavior and its result in the form of trajectory of changes. This book is devoted to dynamics of a wide class of specific but very important objects such as electromechanical systems. This is a very rigorous discipline and has a long tradition, as its theoretical bases were formulated in the first half of the XIX century by d’ Alembert, Lagrange, Hamilton, Maxwell and other prominent scientists, but their crucial results were based on previous pioneering research of others such as Copernicus, Galileo, Newton... This book in its theoretical foundations is based on the principle of least action which governs classical as well as relativistic mechanics and electromagnetism and leads to Lagrange’s equations which are applied in the book as universal method to construct equations of motion of electromechanical systems. It gives common and coherent grounds to formulate mathematical models for all lumped parameters’ electromechanical systems, which are vital in our contemporary industry and civilized everyday life. From these remarks it seems that the book is general and theoretical but in fact it is a very practical one concerning modern electrical drives in a broad sense, including electromechanical energy conversion, induction motor drives, brushless DC drives with a permanent magnet excitation and switched reluctance machines (SRM). And of course their control, which means shaping of their trajectories of motion using modern tools, their designed autonomy in keeping a track according to our programmed expectations. The problems presented in the book are widely illustrated by characteristics, trajectories, dynamic courses all computed by use of developed simulation models throughout the book. There are some classical subjects and the history of the discipline is discussed but finally all modern tools and means are presented and applied. More detailed descriptions follow in abstracts for the particular chapters. The author hopes kind readers will enjoy and profit from reading this book.
Number Theory
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Author : H. Kisilevsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Number Theory written by H. Kisilevsky 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 2004 with Mathematics categories.
Collects articles from the meeting of the Canadian Number Theory Association held at the Centre de Recherches Mathematiques (CRM) at the University of Montreal. This book covers topics such as algebraic number theory, analytic number theory, arithmetic algebraic geometry, computational number theory, and Diophantine analysis and approximation.