Descent and generation for noncommutative coherent algebras over schemes

Abstract

Our work shows forms of descent, in the fppf, h and étale topologies, for strong generation of the bounded derived category of a noncommutative coherent algebra over a scheme. Even for (commutative) schemes this yields new perspectives. As a consequence we exhibit new examples where these bounded derived categories admit strong generators. We achieve our main results by leveraging the action of the scheme on the coherent algebra, allowing us to lift statements into the noncommutative setting. In particular, this leads to interesting applications regarding generation for Azumaya algebras.

arXiv commentCurrent: Major update, obtained strengthened result for the étale topology and improved exposition. Previous: Comments welcome! Some parts of arXiv:2408.04561 have been moved here