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arXiv · 1909.05058

Intersection theories of coherent sheaf stacks and virtual pull-backs via semi-perfect obstruction theories

Sanghyeon Lee
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Abstract

In this paper, we construct proper pushforwards and flat pullbacks in Chow groups of coherent sheaf stacks over a Deligne-Mumford(DM) stack. When there is a relative semi-perfect obstruction theory for a DM-type morphism $X \to Y$, $X$ is a DM stack and $Y$ is a DM stack or a smooth Artin stack, we define a virtual pull-back as a bivariant class. This is an analogue of virtual pull-backs defined by Manolache.

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Sanghyeon Lee. 2019-09-11. Intersection theories of coherent sheaf stacks and virtual pull-backs via semi-perfect obstruction theories. https://arxiv.org/abs/1909.05058

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