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arXiv · 1110.5117

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

Parker E. Lowrey
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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.

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Parker E. Lowrey. 2012-07-05. The moduli stack and motivic Hall algebra for the bounded derived category. https://arxiv.org/abs/1110.5117

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