Abstract Answering a question of Hatcher and Vogtmann, we prove that the top homology group free factor complex is not dualizing module for $\operatorname {Aut}(F_{n})$, at least $n = 5$.

We classify complactly generated t-structures on the derived category of modules over a commutative Noetherian ring R in terms of decreasing filtrations by supports on Spec(R). A decreasing filtration by supports φ : Z → Spec(R) satisfies the weak Cousin condition if for any integer i the set φ(i) contains all the inmediate generalizations of each point in φ(i+ 1). Every t-structure on Dbfg(R) ...

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

We consider rings admitting a Matlis dualizing module E. We argue that if R admits two such dualizing modules, then a module is reflexive with respect to one if and only if it is reflexive with respect to the other. Using this fact we argue that the number (whether finite or infinite) of distinct dualizing modules equals the number of distinct invertible (R,R)-bimodules. We show by example that...

Two distinguished types of semidualizing complexes are the shifts underlying rings and dualizing complexes. Let C be a complex for an analytically irreducible local ring R set n:=supC d:=dimRC. We show that is quasi-isomorphic to shift if only nth Betti number one. Also, we dth Bass

The geometry of the Lubin-Tate space of deformations of a formal group is studied via anétale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of the deformation space which, in turn, yields a formula for the dualizing complex in stable homotopy theory.