ROOM 4: Orders over CM local rings with positive CM dominant dimension

Abstract: I will try to show you that some orders over Cohen-Macaulay local rings have derived dimension bounded above by twice the Krull dimension of the base ring. The main ingredients are a condition on the dominant dimension inside the category of centrally Cohen-Macaulay modules and a condition on the Nakayama functor again on the same category. The first condition gives rise to a canonical tilting module whose endomorphism algebra is nicer if the order we start with has large global dimension. The second condition guarantees that we can iterate this process.The ideas from this work are similar to the works of Hongxing Chen-Changchang Xi and Matthew Pressland-Julia Sauter. However, they reveal new results when the base ring is of positive Krull dimension.This work is still ongoing.

combinatoricscategory theoryrings and algebrasrepresentation theory

Audience: researchers in the topic

( video )

Sherbrooke Meeting on Representation Theory of Algebras, Corona Edition (fully online)

Series comments: Please contact Thomas Brüstle or Juan Carlos Bustamante if you are interested to participate.