## Rigid Local Systems. (AM-139) |

Riemann introduced the concept of a "local system" on P This book is devoted to constructing all (irreducible) rigid local systems on P 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 "It is clear that this book presents highly important new views and results on the classical theory of complex linear differential equations." - 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
- Arithmetic Moduli of Elliptic Curves. (AM-108). [Paperback]
- Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180). [Hardcover and Paperback]
- Exponential Sums and Differential Equations. (AM-124). [Paperback]
- Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116). [Paperback]
- Moments, Monodromy, and Perversity. (AM-159): A Diophantine Perspective. (AM-159). [Paperback]
- Twisted L-Functions and Monodromy. (AM-150). [Paperback]
- Annals of Mathematics Studies
Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors
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