The lattice property for perfect complexes on singular stacks

TL;DR

This paper proves that the complexified noncommutative topological Chern character is an isomorphism for the stable oo-category of perfect complexes on certain singular stacks, extending known results to more general settings.

Contribution

It establishes the isomorphism of the complexified noncommutative topological Chern character for perfect complexes on derived Deligne-Mumford stacks and coherent complexes on derived algebraic spaces.

Findings

The noncommutative topological Chern character is an isomorphism for perfect complexes on derived stacks.

Extension of the isomorphism result to coherent complexes on derived algebraic spaces.

Provides foundational results for the lattice property in the context of singular stacks.

Abstract

Let C be the stable oo-category of perfect complexes on a derived Deligne-Mumford stack X of finite type over the complex numbers. We prove that the complexified noncommutative topological Chern character is an isomorphism for C. In the appendix we show the same property for C the stable oo-category of coherent complexes on a derived algebraic space.