Dualizing complexes and -structures for algebraic spaces
arXiv:2602.20742
summary
The paper proves the existence of dualizing complexes for suitable Deligne–Mumford stacks and uses this to classify all tensor t‑structures on the bounded derived category of coherent sheaves on such stacks.
Abstract
This work is concerned with -structures on Noetherian algebraic spaces admitting dualizing complexes. In particular, we study their behavior in the étale topology. As a consequence, we classify all tensor -structures on their bounded derived category of coherent sheaves.
new results and proofs, focus on algebraic spaces, improved exposition
Topics & keywords
#dualizing complexes#algebraic stacks#deligne–mumford stacks#derived categories#t-structures#tensor t-structuresdualizing complexalgebraic stackDeligne-Mumford stackbounded derived categorytensor t-structurecoherent sheaves