Abstract

An inhomogeneous linear differential equation Ly = f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in terms of cohomology of linear algebraic groups and is computed for abelian differential equations and for regular singular equations. An analogue of Artin reciprocity for abelian differential equations is given. Malgrange’s work on irregularity is reproved in terms cohomology of linear algebraic groups.

Keywords

Galois differential groups, abelian differential extensions, local and global solutions of differential equations

Mathematical Subject Classification

Primary: 34A30

Secondary: 34M15

Authors