For a commutative noetherian ring R,we establish a bijection between the resolving subcategories consisting of finitely generated R-modules of finite projective dimension and the compactly generated t-structures in the unbounded derived category D(R) that contain R[1] in their heart. Under this bijection, the t-structures (U,V) such that the aisle U consists of objects with homology concentrated in degrees < n correspond to the n-cotilting classes in Mod-R. As a consequence of these results, we prove that the little finitistic dimension findimR of R equals an integer n if and only if the direct sum of the first n + 1 terms in a minimal injective coresolution of R is an injective cogenerator of Mod-R.
t-structures and cotilting modules over commutative noetherian rings
ANGELERI, LIDIA;
2014-01-01
Abstract
For a commutative noetherian ring R,we establish a bijection between the resolving subcategories consisting of finitely generated R-modules of finite projective dimension and the compactly generated t-structures in the unbounded derived category D(R) that contain R[1] in their heart. Under this bijection, the t-structures (U,V) such that the aisle U consists of objects with homology concentrated in degrees < n correspond to the n-cotilting classes in Mod-R. As a consequence of these results, we prove that the little finitistic dimension findimR of R equals an integer n if and only if the direct sum of the first n + 1 terms in a minimal injective coresolution of R is an injective cogenerator of Mod-R.
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