Mel and Craig defined "content", which is a heuristic measure of local cohomology, in their joint paper[1]. This idea is that since the top local cohomology with support on I is a directed limit of Ext's, which are killed by a power of I, we should use the generalized length (called quasi-length) to measure each Ext module and take the limit of that. It turns out that although the quasi-length notion is quite hard to compute, the content notion behaves quite well in some "good" cases. I will explain all these notions and give some basic examples. I will also mention some open problems related to these notions. This talk is based on two papers [1] & [2].

[1] Hochster, M., & Huneke, C. (2009). Quasilength, latent regular sequences, and content of local cohomology. Journal of Algebra, 322(9), 3170-3193.
[2] Hochster, M., & Zhang, W. (2017). Content of local cohomology, parameter ideals, and robust algebras. Transactions of the American Mathematical Society, 1.
Speaker(s): Zhan Jiang (University of Michigan)