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arXiv · 2502.09462

Thomason's completion for K-theory and cyclic homology of quotient stacks

Amalendu Krishna·Ritankar Nath
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Abstract

We prove several completion theorems for equivariant K-theory and cyclic homology of schemes with group action over a field. One of these shows that for an algebraic space over a field acted upon by a linear algebraic group, the derived completion of equivariant K'-theory at the augmentation ideal of the representation ring of the group coincides with the ordinary K'-theory of the bar construction associated to the group action. This provides a solution to Thomason's completion problem. For action with finite stabilizers, we show that the equivariant K-theory and cyclic homology have non-equivariant descriptions even without passing to their completions. As an application, we describe all equivariant Hochschild and other homology groups for such actions.

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Amalendu Krishna, Ritankar Nath. 2025-02-13. Thomason's completion for K-theory and cyclic homology of quotient stacks. https://arxiv.org/abs/2502.09462

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