Silting modules and ring epimorphisms

There are well-known constructions relating ring epimor- phisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring epimorphism which we describe explicitly as an idempotent quotient of the endomorphism ring of the Bongartz completion. For heredi- tary rings, this assignment is used to parametrise homological ring epimorphisms by silting modules. We further show that homological ring epimorphisms of a hereditary ring form a lattice which completes the poset of noncrossing partitions in the case of finite dimensional algebras.