PreprintCC BY 4.0arXiv
Fourier--Mukai loci are open and base change
Abstract
We develop a theory of relative (quasi-)perfect complexes for algebraic spaces. Our main result proves that for a pseudocoherent kernel relatively perfect over both factors, the loci where its fiberwise Fourier--Mukai transform is fully faithful or an equivalence are open. The kernel need not be perfect, and these loci commute with Noetherian base change. Moreover, we provide an explicit autoequivalence for elliptic fibrations, and establish that smoothness and Gorensteinness are derived invariants.
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BibTeX
@misc{villalgordo2026fouriermukai,
title = {{Fourier--Mukai loci are open and base change}},
author = {Elías Guisado Villalgordo and Pat Lank},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.01298},
eprint = {2609.01298},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01298},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fourier--Mukai loci are open and base change
AU - Elías Guisado Villalgordo
AU - Pat Lank
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2609.01298
UR - https://arxiv.org/abs/2609.01298
AB - We develop a theory of relative (quasi-)perfect complexes for algebraic spaces. Our main result proves that for a pseudocoherent kernel relatively perfect over both factors, the loci where its fiberwise Fourier--Mukai transform is fully faithful or an equivalence are open. The kernel need not be perfect, and these loci commute with Noetherian base change. Moreover, we provide an explicit autoequivalence for elliptic fibrations, and establish that smoothness and Gorensteinness are derived invariants.
ER -