The uniqueness problem of dg-lifts and Fourier-Mukai kernels

TL;DR

This paper investigates the conditions under which dg-lifts of exact functors and Fourier-Mukai kernels are unique, using A_infty-categorical methods to establish positive results under certain vanishing hypotheses.

Contribution

It provides new insights into the uniqueness problem of dg-lifts and Fourier-Mukai kernels, applying A_infty-categorical techniques to obtain positive results.

Findings

Proves uniqueness of dg-lifts under specific vanishing conditions

Establishes a relationship between dg-lifts and Fourier-Mukai kernels

Employs A_infty-categorical techniques for the analysis

Abstract

We address the uniqueness problem of dg-lifts of exact functors between triangulated categories, and its relationship with the uniqueness problem of Fourier-Mukai kernels. We prove a positive result under a vanishing hypothesis on the functors, employing A_infty-categorical techniques.