
Rigid Local Systems
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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.
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Content
- 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
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