  Domains in infinite jets present the simplest class of diffieties with
boundary. In this note some basic elements of geometry of these domains are
introduced and an analogue of the C-spectral sequence in this context is
studied. This, in particular, allows cohomological interpretation and analysis
of initial data, boundary conditions, etc, for general partial differential
equations and of transversality conditions in calculus of variations. This kind
applications and extensions to arbitrary diffieties will be considered in
subsequent publications.
