Atiyah-Segal theorem for Deligne-Mumford stacks and applications
Algebraic Geometry
2019-10-18 v3
Abstract
We prove an Atiyah-Segal isomorphism for the higher -theory of coherent sheaves on quotient Deligne-Mumford stacks over . As an application, we prove the Grothendieck-Riemann-Roch theorem for such stacks. This theorem establishes an isomorphism between the higher -theory of coherent sheaves on a Deligne-Mumford stack and the higher Chow groups of its inertia stack. Furthermore, this isomorphism is covariant for proper maps between Deligne-Mumford stacks.
Keywords
Cite
@article{arxiv.1701.05047,
title = {Atiyah-Segal theorem for Deligne-Mumford stacks and applications},
author = {Amalendu Krishna and Bhamidi Sreedhar},
journal= {arXiv preprint arXiv:1701.05047},
year = {2019}
}
Comments
Final version (50 pages), to appear in J. Algebraic Geom. (JAG)