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arXiv · 2412.05071

A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks

Utsav Choudhury·Neeraj Deshmukh·Amit Hogadi
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Abstract

We develop a motivic cohomology theory, representable in the Voevodsky's triangulated category of motives, for smooth separated Deligne-Mumford stacks and show that the resulting higher Chow groups are canonically isomorphic to the higher $K$-theory of such stacks. This generalises the Grothendieck-Riemann-Roch theorem to the category of smooth Deligne-Mumford stacks.

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Utsav Choudhury, Neeraj Deshmukh, Amit Hogadi. 2024-12-06. A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks. https://arxiv.org/abs/2412.05071

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