Singularités irrégulières : Correspondance et documents

Author(s): 
P. Deligne, B. Malgrange, J.-P. Ramis
Publisher: 
Société Mathématique de France
Year: 
2007
ISBN: 
978-2-85629-241-9
MSC main category: 
14 Algebraic geometry
Review: 

The book contains a few introductory texts of the authors on an irregular version of Hodge theory, the formal reduction of differential equations with irregular singularities and Gevrey filtration on the Picard-Vessiot group of irregular differential equations. The general theme behind these expositions comprises topics like the theory of linear differential equations with irregular singularities, asymptotics of their solutions, Stokes sheaves and Galois theory of differential fields. However, the core of the book is based on reprints of correspondence among the authors (with a few exceptions) on the topics mentioned above in the period 1976-1991 (with a few exceptions). In this way, an interested reader can gain a direct insight into the evolution of the subject, culminating in applications like the geometric Langlands program.

Reviewer: 
pso