In this paper we study local cohomology of finitely generated bigraded modules over a standard bigraded ring with respect to the irrelevant bigraded ideals and establish a duality theorem. Several applications are considered.
"Local duality for bigraded modules." Illinois J. Math. 51 (1) 137 - 150, Spring 2007. https://doi.org/10.1215/ijm/1258735329