  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 of cohomology of linear
algebraic groups.
