Stability conditions on scheme-derived categories

The scheme-derived category consumers that need Bridgeland stability: bounded-coherent and derived-pullback base change of pre-stability data, the pushforward of stability conditions along bounded coherent pullback, their pullback along bounded coherent direct image, and the action of geometric Fourier--Mukai kernels on stability conditions. It also identifies perfect objects as the geometric test class for mass--Hom bounds.

This is the one subtree below AlgebraicGeometry/DerivedCategory/ that imports the stability tree. The DerivedCategory umbrella deliberately does not re-export it, so Dᵇ(Coh X), Dqc, pullback, and kernels stay importable without stability conditions; the top-level AlgebraicGeometry umbrella imports it. Declarations keep the namespaces of the objects they extend, AlgebraicGeometry.DerivedCategory.Families and AlgebraicGeometry.DerivedCategory.FourierMukai.