Yoga for Fourier--Mukai partnership
Algebraic Geometry
2026-03-27 v3
Abstract
We study the behavior of integral transforms under base change. In particular, we establish a yoga of local algebra and fibers to test for derived equivalences or fully faithfulness via integral transforms. This generalizes a result of Orlov to singular varieties and strengthens several results in the literature by allowing arbitrary base fields. Additionally, it provides new insight into fibrations and their singularities in arithmetic settings (e.g.\ projective and flat schemes over a DVR).
Keywords
Cite
@article{arxiv.2512.16503,
title = {Yoga for Fourier--Mukai partnership},
author = {Elías Guisado Villalgordo and Pat Lank and Kabeer Manali Rahul and Nebojsa Pavic},
journal= {arXiv preprint arXiv:2512.16503},
year = {2026}
}
Comments
Full generalization of Orlov's result, improved applications, new proof strategies, added coauthor; comments welcome!