Rigid Local Systems - Rilegato

Katz, Nicholas M.

Rilegato

ISBN 10: 0691011192 ISBN 13: 9780691011196

Casa editrice: Princeton Univ Pr, 1995

Riassunto

Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to studynth 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 standardnth 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 thel-adic Fourier Transform.

Su questo libro

Recensione:

"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

Contenuti:

• 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

Su questa edizione

• Editore: Princeton Univ Pr
• Data di pubblicazione: 1995
• ISBN 10: 0691011192
• ISBN 13: 9780691011196
• Rilegatura: Copertina rigida
• Numero di pagine: 223