English

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 KK-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