Intuitively, data management and data integration tools should be well-suited for exchanging information in a semantically meaningful way. Unfortunately, they suffer from two significant problems: they typically require a comprehensive schema design before they can be used to store or share information, and they are difficult to extend because schema evolution is heavyweight and may break backwards compatibility. As a result, many small-scale data sharing tasks are more easily facilitated by non-database-oriented tools that have little support for semantics. The goal of the peer data management system (PDMS) is to address this need: we propose the use of a decentralized, easily extensible data management architecture in which any user can contribute new data, schema information, or even mappings between other peers' schemas. PDMSs represent a natural step beyond data integration systems, replacing their single logical schema with an interlinked collection of semantic mappings between peers' individual schemas. This paper considers the problem of schema mediation in a PDMS. Our first contribution is a flexible language for mediating between peer schemas, which extends known data integration formalisms to our more complex architecture. We precisely characterize the complexity of query answering for our language. Next, we describe a reformulation algorithm for our language that generalizes both global-as-view and local-as-view query answering algorithms. Finally, we describe several methods for optimizing the reformulation algorithm, and an initial set of experiments studying its performance.