Graded manifold

Summary

A graded manifold is a smooth manifold whose sheaf of functions is enlarged by anticommuting odd coordinates. Locally its functions are smooth functions of $n$ ordinary variables with values in a Grassmann algebra on $m$ generators. It is the algebraic form, due to Kostant and to Berezin and Leites, of a supermanifold. Graded manifolds give a geometric home to fermionic fields and to the odd variables of the BRST and BV formalisms.