Physical Sciences and Mathematics Commons^™

The Derived Category Of A Locally Complete Intersection Ring, Joshua Pollitz

Department of Mathematics: Dissertations, Theses, and Student Research

Let R be a commutative noetherian ring. A well-known theorem in commutative algebra states that R is regular if and only if every complex with finitely generated homology is a perfect complex. This homological and derived category characterization of a regular ring yields important ring theoretic information; for example, this characterization solved the well-known ``localization problem" for regular local rings. The main result of this thesis is establishing an analogous characterization for when R is locally a complete intersection. Namely, R is locally a complete intersection if and only if each nontrivial complex with finitely generated homology can build a …