Commutative Algebra Seminar

Let R be a commutative noetherian ring. It is well known that R is regular if and only if every complex with finitely generated homology is a perfect complex. The goal of this talk is to explain how one can characterize whether R is locally a complete intersection in terms of how each complex with finitely generated homology relates to the perfect complexes. Namely, R is locally a complete intersection if and only if each nontrivial complex with finitely generated homology can build a nontrivial perfect complex in the derived category using finitely many cones and retracts. This characterization gives a completely triangulated category characterization of locally complete intersection rings. In this talk, we will introduce a theory of support varieties and discuss how they can be applied to yield this characterization. Speaker(s): Josh Pollitz (University of Nebraska -- Lincoln)