Rigid local systems /

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 ranknlocal systems (of local holomorphic solutions) to which they gave rise. His first application was to stu...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Katz, Nicholas M., 1943-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, 1996.
Colección:Annals of mathematics studies ; no. 139.
Temas:
Differential equations > Numerical solutions.
Hypergeometric functions.
Sheaf theory.
Équations différentielles > Solutions numériques.
Fonctions hypergéométriques.
Théorie des faisceaux.
MATHEMATICS > Complex Analysis.
Differential equations > Numerical solutions
Hypergeometric functions
Sheaf theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title
  • Copyright
  • Contents
  • Introduction
  • CHAPTER 1 First results on rigid local systems
  • 1.0 Generalities concerning rigid local systems over C
  • 1.1 The case of genus zero
  • 1.2 The case of higher genus
  • 1.3 The case of genus one
  • 1.4 The case of genus one: detailed analysis
  • CHAPTER 2 The theory of middle convolution
  • 2.0 Transition from irreducible local systems on open sets of P^1 to irreducible middle extension sheaves on A^1
  • 2.1 Transition from irreducible middle extension sheaves on A^1 to irreducible perverse sheaves on A^1
  • 2.2 Review of D^bc(X, Ql)
  • 2.3 Review of perverse sheaves
  • 2.4 Review of Fourier Transform
  • 2.5 Review of convolution
  • 2.6 Convolution operators on the category of perverse sheaves: middle convolution
  • 2.7 Interlude: middle direct images (relative dimension one)
  • 2.8 Middle additive convolution via middle direct image
  • 2.9 Middle additive convolution with Kummer sheaves
  • 2.10 Interpretation of middle additive convolution via Fourier Transform
  • 2.11 Invertible objects on A^1 in characteristic zero
  • 2.12 Musings on *mid -invertible objects in P in the Gm case
  • 2.13 Interlude: surprising relations between *mid on A^1 and on Gm
  • 2.14 Interpretive remark: Fourier-Bessel Transform
  • 2.15 Questions about the situation in several variables
  • 2.16 Questions about the situation on elliptic curves
  • 2.17 Appendix 1: the basic lemma on end-exact functors
  • 2.18 Appendix 2: twisting representations by characters
  • CHAPTER 3 Fourier Transform and rigidity
  • 3.0 Fourier Transform and index of rigidity
  • 3.1 Lemmas on representations of inertia groups
  • 3.2 Interlude: the operation ⊗mid
  • 3.3 Applications to middle additive convolution
  • 3.4 Some open questions about local Fourier Transform
  • CHAPTER 4 Middle convolution: dependence on parameters.

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