Galois Representations Of Orthogonal Rigid Local Systems
DOWNLOAD
Download Galois Representations Of Orthogonal Rigid Local Systems PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Galois Representations Of Orthogonal Rigid Local Systems book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Galois Representations Of Orthogonal Rigid Local Systems
DOWNLOAD
Author : Michael Schulte
language : en
Publisher:
Release Date : 2012
Galois Representations Of Orthogonal Rigid Local Systems written by Michael Schulte and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Rigid Local Systems
DOWNLOAD
Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 1996
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 1996 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.
Galois Groups And Fundamental Groups
DOWNLOAD
Author : Tamás Szamuely
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-16
Galois Groups And Fundamental Groups written by Tamás Szamuely 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 2009-07-16 with Mathematics categories.
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Topics In Galois Theory
DOWNLOAD
Author : Jean-Pierre Serre
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Topics In Galois Theory written by Jean-Pierre Serre and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi
Variations On A Theorem Of Tate
DOWNLOAD
Author : Stefan Patrikis
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-10
Variations On A Theorem Of Tate written by Stefan Patrikis 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 2019-04-10 with Algebraic number theory categories.
Let F be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations Gal(F¯¯¯¯/F)→PGLn(C) lift to GLn(C). The author takes special interest in the interaction of this result with algebraicity (for automorphic representations) and geometricity (in the sense of Fontaine-Mazur). On the motivic side, the author studies refinements and generalizations of the classical Kuga-Satake construction. Some auxiliary results touch on: possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois “Tannakian formalisms” monodromy (independence-of-ℓ) questions for abstract Galois representations.
Algebra 2
DOWNLOAD
Author : Ramji Lal
language : en
Publisher: Springer
Release Date : 2017-05-03
Algebra 2 written by Ramji Lal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-03 with Mathematics categories.
This is the second in a series of three volumes dealing with important topics in algebra. Volume 2 is an introduction to linear algebra (including linear algebra over rings), Galois theory, representation theory, and the theory of group extensions. The section on linear algebra (chapters 1–5) does not require any background material from Algebra 1, except an understanding of set theory. Linear algebra is the most applicable branch of mathematics, and it is essential for students of science and engineering As such, the text can be used for one-semester courses for these students. The remaining part of the volume discusses Jordan and rational forms, general linear algebra (linear algebra over rings), Galois theory, representation theory (linear algebra over group algebras), and the theory of extension of groups follow linear algebra, and is suitable as a text for the second and third year students specializing in mathematics.
Rational Points On Modular Elliptic Curves
DOWNLOAD
Author : Henri Darmon
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Rational Points On Modular Elliptic Curves written by Henri Darmon 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 Curves, Elliptic categories.
The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.
The Eigenbook
DOWNLOAD
Author : Joël Bellaïche
language : en
Publisher: Springer Nature
Release Date : 2021-08-11
The Eigenbook written by Joël Bellaïche and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-11 with Mathematics categories.
This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs. Written in an engaging and educational style, the book also includes exercises and provides their solution.
Lecture Notes In Algebraic Topology
DOWNLOAD
Author : James F. Davis
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-22
Lecture Notes In Algebraic Topology written by James F. Davis and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-22 with Mathematics categories.
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Lectures On K3 Surfaces
DOWNLOAD
Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-26
Lectures On K3 Surfaces written by Daniel Huybrechts 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 2016-09-26 with Mathematics categories.
Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.