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 Milnor squares and usual tensor products over commutative rings, we introduce exact contexts and their noncommutative tensor products, respectively. We then construct universal localizations and characterize when they are homological in terms of the data of exact contexts. In this way we establish new methods to get recollements of derived categories of rings.