Gorenstein D-branes of type B

Let (S; n) be a commutative noetherian local ring and w in n be non-zerodivisor. We propose a natural definition of the category of Gorenstein pairs of w, by replacing projectives with finitely generated Gorenstein projective S-modules in the category of pairs. It is shown that the category of Gorenstein pairs of w is a Frobeius category, and in particular, its projective objects are the same as the category of pairs. The stable category of Gorenstein pairs, which admits a natural structure of a triangulated category, is called Gorenstein D-branes of type B. It is proved that the singularity category of the factor ring R = S=(w) as well as the category of D-branes of type B, can be realized as triangulated subcategories of Gorenstein D-branes of type B. In studying the category of Gorenstein D-branes of type B, the submodule category of Gorenstein projective S-modules has been used appropriately.