%0 Journal Article %T Alexander duality and Stanley depth of multigraded modules %A Ryota Okazaki %A Kohji Yanagawa %J Mathematics %D 2010 %I arXiv %X We apply Miller's theory on multigraded modules over a polynomial ring to the study of the Stanley depth of these modules. Several tools for Stanley's conjecture are developed, and a few partial answers are given. For example, we show that taking the Alexander duality twice (but with different "centers") is useful for this subject. Generalizing a result of Apel, we prove that Stanley's conjecture holds for the quotient by a cogeneric monomial ideal. %U http://arxiv.org/abs/1003.4008v3