HEARTS OF T-STRUCTURES IN THE DERIVED CATEGORY OF A COMMUTATIVE NOETHERIAN RING

摘要

Let R be a commutative Noetherian ring and let D(R) be its (unbounded) derived category. We show that all compactly generated t-structures in D(R) associated to a left bounded filtration by supports of Spec(R) have a heart which is a Grothendieck category. Moreover, we identify all compactly generated t-structures in D(R) whose heart is a module category. As geometric consequences for a compactly generated t-structure (U, U-perpendicular to[1]) in the derived category D(X) of an affine Noetherian scheme X, we get the following: 1) if the sequence (U[-n]n D-<= 0(X))(n is an element of N) is stationary, then the heart H is a Grothendieck category; 2) if H is a module category, then H is always equivalent to Qcoh(Y), for some affine subscheme Y subset of X; 3) if X is connected, then: a) when boolean AND(kappa is an element of Z) U[kappa] = 0, the heart H is a module category if, and only if, the given t-structure is a translation of the canonical t-structure in D(X); b) when X is irreducible, the heart H is a module category if, and only if, there are an affine subscheme Y subset of X and an integer m such that U consists of the complexes U is an element of D(X) such that the support of H-j (U) is in XY, for all j > m.