Riemann introduced the concept of a "local system" on P^{1}{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 ranktwo local systems on P^{1} {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 _{n1}'s, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P^{1}{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 farreaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the ladic Fourier Transform. To view this DRM protected ebook on your desktop or laptop you will need to have Adobe Digital Editions installed. It is a free software. We also strongly recommend that you sign up for an AdobeID at the Adobe website. For more details please see FAQ 1&2. To view this ebook on an iPhone, iPad or Android mobile device you will need the Adobe Digital Editions app, or BlueFire Reader or Txtr app. These are free, too. For more details see this article.
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Ebook Details 

Pages:  219 
Size:  12.3 MB 
Publisher:  Princeton University Press 
Date published:  2016 
ISBN:  9781400882595 (DRMPDF)

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Copying:  not allowed  Printing:  not allowed  Read Aloud:  not allowed 
