Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces

Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S is simply connected and a universal sheaf E exists over S×M, then its class [E] admits a Künneth decomposition as a class in the tensor product of the topological K-rings. The generators are the Chern classes of the Künneth factors of [E] in . The general case is similar.