The Sally Modules of Ideals: A Survey

The Sally module of a Rees algebra $\BB$ relative to one of its Rees subalgebras $\AA$ is a construct that can be used as a mediator for the trade-off of cohomological (e.g. depth) information between $\BB$ and the corresponding associated graded ring for several types of filtrations. While originally devised to deal with filtrations of finite colength, here we treat aspects of these developments for filtrations in higher dimensions as well.