Seminar

Zoom Link

A celebrated theorem in commutative algebra is the Auslander-Buchsbaum, Serre Theorem which states that a commutative noetherian local ring is regular if and only if every module over that ring has finite projective dimension. One can reinterpret this theorem in the derived category by stating that a commutative noetherian local ring is regular if and only if every object in the derived category of that ringwith bounded homology is perfect. In 2018, Josh Pollitz gave a similar flavor of theorem by classifying complete intersections using the derived category of that ring. In this talk I will go over the statement of the theorem and the relevant background information needed to understand the statement. In addition, I'll talk about these objects called cohomological support varieties and the pivotal role they play in the proof of his theorem. 

Cohomological Support Varieties and the Derived Category of a Complete Intersection