Cohen-Macaulayness and squarefree modules

In this paper we consider the category of squarefree modules over the polyn omial ring and an exact duality functor, which is an extension of the Alexa nder dual of a simplicial complex. We give a relationship between the squar efree components of local cohomology groups of a squarefree module and the Tor groups of its dual, With this result it is shown that a squarefree modu le is sequentially Cohen-Macaulay if and only if the dual is componentwise linear.