A remark on Continuous K-theory and Fourier-Sato transform

TL;DR

This paper generalizes Efimov's computation of the universal localizing invariant for sheaf categories with microsupport constraints using Fourier-Sato transform, and applies it to Novikov toric schemes.

Contribution

It introduces a new proof technique via Fourier-Sato transform for computing localizing invariants, extending Efimov's results.

Findings

Generalized Efimov's computation for sheaf categories

Applied the method to Novikov toric schemes

Provided categorical equivalences using Fourier-Sato transform

Abstract

In this note, we prove a generalization of Efimov's computation for the universal localizing invariant of categories of sheaves with certain microsupport constraints. The proof is based on certain categorical equivalences given by the Fourier-Sato transform, which is different from the original proof. As an application, we compute the universal localizing invariant of the category of almost quasi-coherent sheaves on the Novikov toric scheme introduced by Vaintrob.