Algebraic $K$-theory of stably compact spaces

TL;DR

This paper computes algebraic K-theory and other localizing invariants for categories of sheaves over stably locally compact spaces, generalizing previous results for special classes of spaces.

Contribution

It provides a unified formula for localizing invariants on sheaf categories over stably compact spaces, extending known cases.

Findings

Unified formula for localizing invariants on sheaf categories

Generalizes K-theory calculations for various space classes

Recovers several known K-theory results as special cases

Abstract

We compute the value of finitary localizing invariants, including algebraic $K$-theory, on categories of sheaves over stably locally compact spaces $X$. Our formula simultaneously generalizes the cases of locally compact Hausdorff and coherent (spectral) spaces and recovers several smaller $K$-theory calculations as special instances.