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In this paper, we answer a question of Dwyer, Greenlees, and Iyengar by proving a local ring $R$ is a complete intersection if and only if every complex of $R$-modules with finitely generated homology is proxy small. Moreover, we establish that a commutative noetherian ring $R$ is locally a complete intersection if and only if every complex of $R$-modules with finitely generated homology is virtually small.
We give an exposition and generalization of Orlovs theorem on graded Gorenstein rings. We show the theorem holds for non-negatively graded rings which are Gorenstein in an appropriate sense and whose degree zero component is an arbitrary non-commutat
Let $(A,mathfrak{m})$ be a complete intersection with $k = A/mathfrak{m}$ algebraically closed. Let CMS(A) be the stable category of maximal CM $A$-modules. For a large class of thick subcategories $mathcal{S}$ of CMS(A) we show that there is a theor
In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of $bz^noplus T$ with no invertible elements, where $T$ is a finite abelian group. We also ch
We characterize the graphs $G$ for which their toric ideals $I_G$ are complete intersections. In particular we prove that for a connected graph $G$ such that $I_G$ is complete intersection all of its blocks are bipartite except of at most two. We pro
Our purpose is to study the family of simple undirected graphs whose toric ideal is a complete intersection from both an algorithmic and a combinatorial point of view. We obtain a polynomial time algorithm that, given a graph $G$, checks whether its