Speaker: Isaac Bird (University of Manchester)
Title: Cotilting with balanced big Cohen-Macaulay modules
Abstract: Over a Cohen-Macaulay local ring the class of balanced big Cohen-Macaulay modules, as introduced by Hochster, provides an intuitive way to extend the class of maximal Cohen-Macaulay modules beyond finitely generated modules. We consider the definable closure of this class, show that it is cotilting and use this to describe the minimal injective resolutions of balanced big Cohen-Macaulay modules. This furthers a classic result of R. Sharp. We then illustrate how, in certain cases, this result extends beyond the local case and give an application for Gorenstein flat modules over commutative Gorenstein rings. We contrast this situation by considering the cotilting class formed by taking modules of maximal Ext depth. We give a description of this class and its cotilting structure, including providing a cotilting module. This will cumulate in giving a classification of all cotilting classes containing both the maximal, and balanced big, Cohen-Macaulay modules.