Silting modules

We introduce the new concept of silting modules. These modules generalize tilting modules over an arbitrary ring, as well as support τ-tilting modules over a finite dimensional algebra recently introduced by Adachi, Iyama, and Reiten. We show that silting modules generate torsion classes that provide left approximations, and that every partial silting module admits an analog of the Bongartz complement. Furthermore, we prove that silting modules are in bijection with 2-term silting complexes and with certain t-structures and co-t-structures in the derived module category. We also see how some of these bijections hold for silting complexes of arbitrary finite length.