Morphisms Of Affine Schemes And Equivalence Of Categories

Abstract

In this work we construct the relation between the category R-filt (G(R)-gr) and the category O^ — Filt(O^ — Gr). The quantum (ungraded) version of this result can be obtained by restricting to parts of zero degree. Geometrically, we summarize geometrical properties for the affine scheme spec8 G(R). Finally, in the language of formal affine schemes we obtain the relation between R-filt (G(R)-gr) and the category O £ - Filt(O ^ - Gr). The results have a special meaning for sheaves of rings of differential operators.