The moduli stack and motivic Hall algebra for the bounded derived category

Abstract

We give an alternate formulation of pseudo-coherence over an arbitrary derived stack X. The full subcategory of pseudo-coherent objects forms a stable sub-infinity-category of the derived category associated to X. Using relative Tor-amplitude we define a derived stack classifying pseudo-coherent objects. For reasonable base schemes, this classifies the bounded derived category. In the case that X is a projective derived scheme flat over the base, we show the moduli is locally geometric and locally of almost finite type. Using this result, we prove the existence of a derived motivic Hall algebra associated to X.

Citations fixed

References in corpus (6)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Derived Algebraic Geometry V: Structured Spaces
• Thom-Sebastiani & Duality for Matrix Factorizations
• Stable Infinity Categories
• Grothendieck rings of Artin n-stacks
• Derived moduli of schemes and sheaves

Cited by in corpus (1)

• Grothendieck-Riemann-Roch for derived schemes