Lifting Ore Sets of Noetherian Filtered Rings and Applications Original Research Article

LetRbe a filtered ring such that the Rees ringRofRis left Noetherian. It is observed that ifTis a left Ore set of the associated graded ringG(R) consisting of homogeneous elements then the saturated setS={sset membership, variantR, σ(s)set membership, variantT} is a left Ore set ofR. This lifting property is used to obtain local-global results onRwhich simplify some microlocal-global results in the literature. IfG(R) is positively graded and commutative then certain structure sheaves onRare constructed.