Title: Embedding Theorems for Modules and Behavior of Closure Operations
Abstract: We prove several theorems about embeddings of modules that give new proofs of comparison theorems for tight closure and plus closure, providing both a different perspective and stronger results. As a consequence, we obtain at once comparison results for several analogues of tight closure that have been defined much more recently. Part of the talk will give an exposition of the theory of modules of finite G-dimension: no background about this will be assumed. What we need about closures will also be explained. The new results are all joint work with Yongwei Yao.
