Study on Chohomology of supermanifolds - Ahmed, M. Khondokar (BRAC University, 2010)
In this present paper de Rham cohomology of graded manifolds, cohomology of graded differential forms and cohomology of DeWitt supermanifolds are studied. The structure of a G-supermanifold in general is not acyclic. So, the cohomology is defined via the complex of graded differential forms. This situation is investigated together with the graded Dolbeault cohomology of complex G-supermanifolds. A theorem is established that the structure sheaf of any DeWitt G-supermanifold is acyclic.