exact contexts and recollements of derived module categories

This talk surveys some of our recent joint works on construc-tions of recollements of derived categories of algebras. generalising milnorsquares and usual tensor products over commutative rings, we introduce exactcontexts and their noncommutative tensor products, respectively. we thenconstruct universal localizations and characterize when they are homologicalin terms of the data of exact contexts. in this way we establish new methodsto get recollements of derived categories of rings.