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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
1996.
|
| Colección: | Annals of mathematics studies ;
no. 139. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Katz, Nicholas M., |d 1943- | |
| 245 | 1 | 0 | |a Rigid local systems / |c by Nicholas M. Katz. |
| 260 | |a Princeton, N.J. : |b Princeton University Press, |c 1996. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a The Annals of mathematics studies ; |v no. 139 | |
| 504 | |a Includes bibliographical references (pages 219-223). | ||
| 520 | |a 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 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,nFn-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.eISBN: 978-1-4008-8259-5 | ||
| 505 | 0 | |a 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. | |
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Differential equations |x Numerical solutions. | |
| 650 | 0 | |a Hypergeometric functions. | |
| 650 | 0 | |a Sheaf theory. | |
| 650 | 6 | |a Équations différentielles |x Solutions numériques. | |
| 650 | 6 | |a Fonctions hypergéométriques. | |
| 650 | 6 | |a Théorie des faisceaux. | |
| 650 | 7 | |a MATHEMATICS |x Complex Analysis. |2 bisacsh | |
| 650 | 7 | |a Differential equations |x Numerical solutions |2 fast | |
| 650 | 7 | |a Hypergeometric functions |2 fast | |
| 650 | 7 | |a Sheaf theory |2 fast | |
| 653 | 0 | |a Differential equations |a Numerical solutions | |
| 653 | 0 | |a Hypergeometric functions | |
| 653 | 0 | |a Sheaf theory | |
| 776 | 0 | 8 | |i Print version: |a Katz, Nicholas M., 1943- |t Rigid local systems. |d Princeton, N.J. : Princeton University Press, 1996 |w (DLC) 95044041 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 139. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt1bd6kqs |z Texto completo |
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