  All kinds of global correspondences of Langlands are evaluated from the
functional representation spaces of the algebraic bilinear semigroups GL2(.x.)
with entries in products,right by left,of sets of archimedean increasing
completions. Degenerate singularities on these functional representation spaces
can give rise,by versal deformations and blowups of these,to one or two new
covering functional representation spaces of GL2(.x.) according to the type of
considered singularities. The discovered correspondences of Langlands are
associated with singular and nonsingular universal GL(2)-structures.
