ZOOM-Link: https://wwu.zoom.us/j/65824696522?pwd=QlpFRkFMZG92RzNXNnRETHFRRXJGQT09#success Meeting-ID: 65824696522 Kenncode: 151702 Abstract: We construct a derived variant of Emerton's eigenvarieties using the locally analytic representation theory of p-adic groups. The main innovations include comparison and exploitation of two homotopy equivalent completed complexes associated to the locally symmetric spaces of a quasi-split reductive group ?, comparison to overconvergent cohomology, proving exactness of finite slope part functor, together with some representation-theoretic statements. As a global application, we exhibit an eigenvariety coming from data of GLn over a CM field as a subeigenvariety for a quasi-split unitary group.