Bondal--Orlov reconstruction for tame stacks with trivial generic stabilizer

Abstract: We generalize the Bondal--Orlov Reconstruction Theorem to smooth, proper, tame algebraic stacks with generically trivial stabilizer, whose canonical bundles are nowhere torsion: They do not become trivial after pullback along any finite morphism from a projective curve. Our main tools are coherent Tannaka duality as proved by Lurie and by Hall and Rydh, and Grothendieck duality for proper tame stacks as developed by Hall and Priver. We additionally use the notion of nowhere torsion line bundle on a scheme to prove a version of the Bondal--Orlov Reconstruction Theorem for finite type, separated, Gorenstein schemes which are not necessarily proper, which generalizes work of Ballard, Favero, Ito, and Matsui.