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

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

2011-10-24

arxiv.org/abs/1110.5117v2

Mathematics

Algebraic Geometry

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Scientific paper

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.

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