Gelfand-Fuchs cohomology for affine superspaces A^(m,n)

We study the cohomology of Lie superalgebra of vector fields on affine super-spaces Am,n with trivial coefficients. In this paper we extend the methodology developed in the previous paper (arXiv:2210.16585) to perform the calculation for arbitrary dimensions $(m, n)$ with m ≥ n. This combined with previously known results for other dimensions $(m, n)$ fully settles the local problem of Gelfand-Fuchs cohomology with trivial coefficients for super-manifolds. As part of the proof we also compute the cohomology of Lie superalgebras gl(m,n) with coefficients given by Schur functors of the standard representation.