6 papers
Reflexivity and ring homomorphisms of finite flat dimension
Anders Frankild, Sean Sather-Wagstaff
In this paper we present a systematic study of the reflexivity properties of homologically finite complexes with respect to semidualizing complexes in the setting of nonlocal rings…
The set of semidualizing complexes is a nontrivial metric space
Anders Frankild, Sean Sather-Wagstaff
We show that the set $\s(R)$ of shift-isomorphism classes of semidualizing complexes over a local ring admits a nontrivial metric. We investigate the interplay between the metr…
Characterizing local rings via homological dimensions and regular sequences
Shokrollah Salarian, Sean Sather-Wagstaff, Siamak Yassemi
Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If G_C-dimension of M/IM is finite for…
Complete intersection dimension for complexes
Sean Sather-Wagstaff
We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties ana…
G-dimension over local homomorphisms. Applications to the Frobenius endomorphism
Srikanth Iyengar, Sean Sather-Wagstaff
We develop a theory of G-dimension for modules over local homomorphisms which encompasses the classical theory of G-dimension for finite modules over local rings. As an application…
Multiplicities and a dimension inequality for unmixed modules
Sean Sather-Wagstaff
We prove the following result, which is motivated by the recent work of Kurano and Roberts on Serre's positivity conjecture. Assume that (R,m) is a local ring with finitely-generat…