Speaker
Description
We study Cohen-Macaulay representations over (not necessarily commutative) Gorenstein rings by using the tilting theory of singularity categories. We study Artin-Schelter Gorenstein algebras A of dimension one including singular Calabi-Yau algebras and classical Gorenstein orders. We prove that the generically projective Z-graded singularity category of A always admits an (explicitly described) silting object, and admits a tilting object if and only if either A is regular or a certain homological invariant g of A (called the average Gorenstein parameter) is non-positive. These results recover our previous results for commutative Gorenstein rings with Buchweitz and Yamaura. We explain our results by giving some examples. This is a joint work with Yuta Kimura and Kenta Ueyama.
