Book Search:  

 

 
Google full text of our books:

bookjacket

Rigid Local Systems. (AM-139)
Nicholas M. Katz

Paperback | 1995 | $78.50 / £55.00 | ISBN: 9780691011189
219 pp. | 6 x 9
| SHOPPING CART

Reviews | Table of Contents

Google full text of this book:
 

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.

Review:

"It is clear that this book presents highly important new views and results on the classical theory of complex linear differential equations."--Zentralblatt für Mathematik

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

Other Princeton books authored or coauthored by Nicholas M. Katz:

Series:

Subject Area:

VISIT OUR MATH WEBSITE

Hardcover: Not for sale in Japan

Shopping Cart:

  • For hardcover/paperback orders:

    For hardcover/paperback orders in the United States, Canada, Latin America, Asia, and Australia

    Paperback: $78.50 ISBN: 9780691011189

    For hardcover/paperback orders in Europe, Africa, the Middle East, India, and Pakistan

    Paperback: £55.00 ISBN: 9780691011189

    Add to shopping cart

    Prices subject to change without notice

    File created: 9/23/2014

Questions and comments to: webmaster@press.princeton.edu
Princeton University Press

New Book E-mails
New In Print
PUP Blog
Videos/Audios
Princeton APPS
Sample Chapters
Subjects
Series
Catalogs
Princeton Legacy Library
Textbooks
Media/Reviewers
Class Use
Rights/Permissions
Ordering
Recent Awards
Princeton Shorts
Freshman Reading
PUP Europe
About Us
Contact Us
Links
F.A.Q.
MATH SITE
PUP Home


Bookmark and Share
Send me emails
about new books in:
Mathematics
More Choices
Email:
Country:
Name: