Murakami Sale
 
 

Recently Viewed clear list


The Powell's Playlist | August 6, 2014

Graham Joyce: IMG The Powell’s Playlist: Graham Joyce



The Ghost in the Electric Blue Suit is set on the English coast in the hot summer of 1976, so the music in this playlist is pretty much all from the... Continue »
  1. $17.47 Sale Hardcover add to wish list

spacer
Qualifying orders ship free.
$88.25
New Trade Paper
Ships in 1 to 3 days
Add to Wishlist
available for shipping or prepaid pickup only
Available for In-store Pickup
in 7 to 12 days
Qty Store Section
25 Remote Warehouse Mathematics- Differential Equations

Other titles in the Annals of Mathematics Studies series:

Rigid Local Systems. (Am-139) (Annals of Mathematics Studies)

by

Rigid Local Systems. (Am-139) (Annals of Mathematics Studies) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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, nFn-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.

Table of Contents

  • First results on rigid local systems
  • The theory of middle concolution
  • Fourier Transform and rigidity
  • Middle concolution: dependence on parameters
  • Structure of rigid local systems
  • Existence algorithms for rigids
  • Diophantine aspects of rigidity
  • rigids

Product Details

ISBN:
9780691011189
Author:
Katz, Nicholas M.
Publisher:
Princeton University Press
Location:
Princeton, N.J. :
Subject:
General
Subject:
Differential Equations
Subject:
Geometry - General
Subject:
Numerical solutions
Subject:
Hypergeometric functions.
Subject:
Sheaf theory.
Subject:
Advanced
Subject:
Mathematics
Subject:
Differential equations -- Numerical solutions.
Subject:
Geometry - Non-Euclidean
Subject:
Mathematics-Differential Equations
Copyright:
Edition Description:
Trade paper
Series:
Annals of Mathematics Studies (Paperback)
Series Volume:
(AM-139)
Publication Date:
December 1995
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
219
Dimensions:
9 x 6 in 12 oz

Other books you might like

  1. Fourier Transforms. (Am-19) (Annals... New Trade Paper $71.25
  2. Annals of Mathematics Studies #151:... New Trade Paper $96.50
  3. Annals of Mathematics Studies #147:... New Trade Paper $82.75

Related Subjects

History and Social Science » Economics » General
History and Social Science » Politics » United States » Politics
Reference » Science Reference » General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry

Rigid Local Systems. (Am-139) (Annals of Mathematics Studies) New Trade Paper
0 stars - 0 reviews
$88.25 In Stock
Product details 219 pages Princeton University Press - English 9780691011189 Reviews:
"Synopsis" by , 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, nFn-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.

spacer
spacer
  • back to top
Follow us on...




Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.