Time: 9:30 - 11:00, March 08, 2023.

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: A Noetherian local ring $(R,m)$ is called Buchsbaum if the difference $length(R/fq)-e(fq, R)$, where $fq$ is an ideal generated by a system of parameters, is a constant independent of $fq$. In this article, we study the tight closure analog of this condition. We prove that in an unmixed excellent local ring $(R,m)$ of prime characteristic $p>0$ and dimension at least one, the difference $e(fq, R)-length(R/fq^*)$ is independent of $fq$ if and only if the parameter test ideal $tau_{pa}(R)$ contains $m$. This is a joint work with Linquan Ma.