Regularity and bounded $t$-structures for algebraic stacks

Abstract: Our work shows (the expected) cohomological characterization for regularity of (Noetherian) algebraic stacks; such a stack is regular if and only if all complexes with bounded and coherent cohomology are perfect. This naturally enables us to extend various statements known for schemes to algebraic stacks. In particular, the conjectures by Antieau--Gepner--Heller and Bondal--Van den Bergh, both resolved for schemes by Neeman, are proven for suitable algebraic stacks.