t-Structures and cotilting modules over commutative noetherian rings

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 (mathcal {D}(R)) that contain (R[1]) in their heart. Under this bijection, the t-structures ((mathcal U,mathcal V)) such that the aisle (mathcal U) consists of objects with homology concentrated in degrees ( correspond to the (n) -cotilting classes in ({{mathrm{Mod}text {-}R}}) . As a consequence of these results, we prove that the little finitistic dimension findim (R) of (R) equals an integer (n) if and only if the direct sum (bigoplus _{k=0}^n E_k(R)) of the first (n+1) terms in a minimal injective coresolution (0rightarrow Rrightarrow E_0(R)rightarrow E_1(R)rightarrow cdots ) of (R) is an injective cogenerator of ({{mathrm{Mod}text {-}R}}) .