A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks
Algebraic Geometry
2025-05-30 v2 K-Theory and Homology
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 -theory of such stacks. This generalises the Grothendieck-Riemann-Roch theorem to the category of smooth Deligne-Mumford stacks.
Keywords
Cite
@article{arxiv.2412.05071,
title = {A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks},
author = {Utsav Choudhury and Neeraj Deshmukh and Amit Hogadi},
journal= {arXiv preprint arXiv:2412.05071},
year = {2025}
}
Comments
New section added on some computations. 13 pages. Comments welcome