Derived equivalences induced by good silting complexes

Simion Breaz, George Ciprian Modoi

Published 2017-07-23Version 1

Consider a (possibly big) silting object $U$ in a derived category over a (dg-)algebra $A$. Under some fairly general appropriate hypotheses, we show that it induces derived equivalences between the derived category over $A$ and a localization of the derived category of dg-endomorphism algebra $B$ of $U$. If, in addition, $U$ is small then this localization is the whole derived category over $B$. We also study the way in which these equivalences restrict to some subcategories of module categories, providing a correspondent for the celebrated Tilting Theorem.