Higher K-theory of Toric stacks

TL;DR

This paper develops spectral sequence techniques to compute higher K-theory of toric stacks, providing explicit descriptions and demonstrating degeneration in many cases for efficient calculations.

Contribution

It introduces spectral sequence methods for higher K-theory of toric stacks and shows their degeneration, enabling explicit computations for many cases.

Findings

Spectral sequences degenerate for many toric stacks.

Explicit descriptions of higher K-theory for smooth toric stacks.

Higher K-theory of toric stack bundles over smooth schemes is characterized.

Abstract

In this paper, we develop several techniques for computing the higher G-theory and K-theory of quotient stacks. Our main results for computing these groups are in terms of spectral sequences. We show that these spectral sequences degenerate in the case of many toric stacks, thereby providing an efficient computation of their higher K-theory. We apply our main results to give explicit description for the higher K-theory for many smooth toric stacks. As another application, we describe the higher K-theory of toric stack bundles over smooth base schemes.