Cosimplicial meromorphic functions cohomology on complex manifolds

Developing ideas of [B. L. Feigin, Conformal field theory and cohomologies the Lie algebra holomorphic vector fields on a complex curve, in Proc. Int. Congress Mathematicians (Kyoto, 1990), Vols. 1 2 (Mathematical Society Japan, Tokyo, 1991), pp. 71–85], we introduce canonical cosimplicial cohomology meromorphic functions for infinite-dimensional formal series with prescribed analytic behavior domains manifold [Formula: see text]. Graded differential sheaf algebras text] via text]-formal any covering by Stein spaces is computed. A relation between (on special set open text]) an singular auxiliary associated to text]-module found. Finally, multiple applications conformal theory, deformation foliations are proposed.