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arXiv · 1701.05047

Atiyah-Segal theorem for Deligne-Mumford stacks and applications

Amalendu Krishna·Bhamidi Sreedhar
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Abstract

We prove an Atiyah-Segal isomorphism for the higher $K$-theory of coherent sheaves on quotient Deligne-Mumford stacks over $\C$. As an application, we prove the Grothendieck-Riemann-Roch theorem for such stacks. This theorem establishes an isomorphism between the higher $K$-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.

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Amalendu Krishna, Bhamidi Sreedhar. 2017-01-18. Atiyah-Segal theorem for Deligne-Mumford stacks and applications. https://arxiv.org/abs/1701.05047

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