On the K-theory of Toric Stack Bundles

TL;DR

This paper computes the Grothendieck K-theory of simplicial toric stack bundles and investigates the Chern character homomorphism, advancing understanding of their algebraic K-theoretic properties.

Contribution

It provides explicit calculations of K-theory for simplicial toric stack bundles and analyzes the Chern character map, a novel contribution in the field.

Findings

Explicit K-theory formulas for simplicial toric stack bundles

Insights into the structure of the Chern character homomorphism

Enhanced understanding of algebraic K-theory in stack bundles

Abstract

Simplicial toric stack bundles are smooth Deligne-Mumford stacks over smooth varieties with fibre a toric Deligne-Mumford stack. We compute the Grothendieck $K$-theory of simplicial toric stack bundles and study the Chern character homomorphism.