Peder Thompson: Acyclic complexes and regular rings

Abstract: Regular rings are characterized by finiteness of projective dimension. For local commutative noetherian rings, this is a classic result in homological algebra. For noetherian rings more generally, Iacob and Iyengar recently characterized regularity in terms of the triviality of certain acyclic complexes. We extend this idea to coherent rings, and prove the equivalence of many acyclicity conditions along the way. This is joint work with Christensen and Estrada.