Rigid Local Systems. (AM-139), Volume 139

Rigid Local Systems. (AM-139), Volume 139
Author :
Publisher : Princeton University Press
Total Pages : 233
Release :
ISBN-10 : 9781400882595
ISBN-13 : 1400882591
Rating : 4/5 (591 Downloads)

Book Synopsis Rigid Local Systems. (AM-139), Volume 139 by : Nicholas M. Katz

Download or read book Rigid Local Systems. (AM-139), Volume 139 written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2016-03-02 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Rigid Local Systems. (AM-139), Volume 139 Related Books

Rigid Local Systems. (AM-139), Volume 139
Language: en
Pages: 233
Authors: Nicholas M. Katz
Categories: Mathematics
Type: BOOK - Published: 2016-03-02 - Publisher: Princeton University Press

GET EBOOK

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 equa
Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
Language: en
Pages: 753
Authors: Gebhard Böckle
Categories: Mathematics
Type: BOOK - Published: 2018-03-22 - Publisher: Springer

GET EBOOK

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental M
Galois Theory of Linear Differential Equations
Language: en
Pages: 446
Authors: Marius van der Put
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

GET EBOOK

From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as th
The Abel Prize 2008-2012
Language: en
Pages: 561
Authors: Helge Holden
Categories: Mathematics
Type: BOOK - Published: 2014-01-21 - Publisher: Springer Science & Business Media

GET EBOOK

Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: · John G. Thompson and Jacques Tits, 2008 · Mikhail Gr
Surveys on surgery theory : papers dedicated to C.T.C. Wall.
Language: en
Pages: 452
Authors: Sylvain Cappell
Categories:
Type: BOOK - Published: 2000 - Publisher: Princeton University Press

GET EBOOK