This paper is an expanded version of three talks given by I. Peeva during the Introductory
Workshop in Commutative Algebra at MSRI in August 2013. It is a survey on infinite graded …

In 2007 Huneke and Wiegand announced in an erratum that one of the conclusions of their
depth formula theorem is flawed due to an incorrect convention for the depth of the zero …

Given a graded-commutative ring acting centrally on a triangulated category, our main result
shows that if cohomology of a pair of objects of the triangulated category is finitely generated …

In this paper we study a long-standing conjecture of Huneke and Wiegand which is
concerned with the torsion submodule of certain tensor products of modules over one …

For finitely generated modules M and N over a Gorenstein local ring R, one has depth M+
depth N= depth (M⊗ RN)+ depth R, ie, the depth formula holds, if M and N are Tor …

Let $ R $ be a Noetherian local ring, and let $ C $ be a semidualizing $ R $-module. In this
paper, we present some results concerning to vanishing of $\operatorname {Ext} $ and finite …

In this paper, we consider a depth inequality of Auslander which holds for finitely generated
Tor-rigid modules over commutative Noetherian local rings. We raise the question of …

Let kk be an algebraically closed field and A be a finitely generated, centrally finite,
nonnegatively graded (not necessarily commutative) k k-algebra. In this note we construct a …

According to the Grothendieck-Lefschetz theorem from SGA 2, there are no nontrivial line
bundles on the punctured spectrum $ U_R $ of a local ring $ R $ that is a complete …

Let $ R $ be a commutative Noetherian Cohen-Macaulay local ring that has positive
dimension and prime characteristic. Li proved that the tensor product of a finitely generated …