Rigid Local Systems. (AM-139), Volume 139 /

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...

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Bibliographic Details
Main Author:	Katz, Nicholas M., 1943- (Author, http://id.loc.gov/vocabulary/relators/aut)
Corporate Author:	De Gruyter
Format:	Book
Language:	English
Published:	Princeton, NJ : Princeton University Press, [2016]
Series:	Annals of mathematics studies ; 139
Subjects:	Differential equations > Numerical solutions Hypergeometric functions Sheaf theory Additive group Alexander Grothendieck Algebraic closure Algebraic differential equation Algebraically closed field Algorithm Analytic continuation Automorphism Axiom of choice Bernhard Riemann Big O notation Calculation Carlos Simpson Coefficient Cohomology Commutator Compactification (mathematics) Comparison theorem Complex analytic space Complex conjugate Complex manifold Conjecture Conjugacy class Convolution Corollary Cube root Cusp form De Rham cohomology Differential equation Dimension Dimensional analysis Discrete valuation ring Disjoint union Divisor Duality (mathematics) Eigenfunction Eigenvalues and eigenvectors Elliptic curve Equation Equivalence of categories Exact sequence Existential quantification Finite field Finite set Fourier transform Functor Fundamental group Generic point Ground field Hodge structure Hypergeometric function Integer Invertible matrix Isomorphism class Jordan normal form Level of measurement Linear differential equation Local system Mathematical induction Mathematics Matrix (mathematics) Monodromy Monomial Morphism Natural filtration Parameter Parity (mathematics) Perfect field Perverse sheaf Polynomial Prime number Projective representation Projective space Pullback (category theory) Pullback Rational function Regular singular point Relative dimension Residue field Ring of integers Root of unity Sequence Sesquilinear form Set (mathematics) Sheaf (mathematics) Six operations Special case Subgroup Subobject Subring Suggestion Summation Tensor product Theorem Theory Topology Triangular matrix Trivial representation Vector space Zariski topology Dictionaries

Table of Contents:

Frontmatter
Contents
Introduction
CHAPTER 1. First results on rigid local systems
CHAPTER 2. The theory of middle convolution
CHAPTER 3. Fourier Transform and rigidity
CHAPTER 4. Middle convolution: dependence on parameters
CHAPTER 5. Structure of rigid local systems
CHAPTER 6. Existence algorithms for rigids
CHAPTER 7. Diophantine aspects of rigidity
CHAPTER 8. Motivic description of rigids
CHAPTER 9. Grothendieck's p-curvature conjecture for rigids
References

Rigid Local Systems. (AM-139), Volume 139 /

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