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Irregular singularities. Correspondence and documents. (Singularités irrégulières. Correspondance et documents.) (French) Zbl 1130.14001

Documents Mathématiques 5. Paris: Société Mathématique de France (ISBN 978-2-85629-241-9/hbk). x, 188 p. (2007).
This volume consists of two parts. The first one is a collection of letters exchanged mostly by P. Deligne, B. Malgrange and J.-P. Ramis covering essentially the period 1976-1991. They discuss the irregular singularities of linear differential equations: asymptotic expansions, Stokes sheaves, moduli, Galois and wild \(\pi_1\). The second part consists of the following previously unpublished papers: 1. B. Malgrange, On the formal reduction of differential equations with irregular singularities (1979); 2. P. Deligne, Irregular Hodge Theory (first version 1984 and second version 2006); 3. J.-P. Ramis, Gevrey filtration on the Picard-Vessiot group of an irregular differential equation (1985); 4. J.-P. Ramis, Construction of privileged semi-canonical bases (1988). The book ends with a large number of notes added by the authors and a list of related references published after the letters have been written. The whole volume has a great historical interest and, in the same time, touches some open central problems in the area which will surely attract a lot of attention in the near future.

MSC:

14-03 History of algebraic geometry
32-03 History of several complex variables and analytic spaces
01A60 History of mathematics in the 20th century
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
34M40 Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain
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