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2025-05-30 10:01:18

This https://arxiv.org/abs/2412.05071 has been replaced.
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A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks
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.