Countability of relative Fourier–Mukai partners
Abstract
Anel and Toën proved that a smooth projective complex variety has only countably many smooth projective Fourier–Mukai partners up to isomorphism. This is generalized in the Stacks Project to the case where the varieties are smooth proper over an arbitrary algebraically closed field. This article will upgrade the proof of the latter reference to show that a smooth proper scheme over a noetherian base has only countably many relative Fourier–Mukai partners up to isomorphism.
Fields of Study & Subjects
Advanced Topology and Set Theory
Mathematical Dynamics and Fractals
advanced mathematical theories
Publication details
- Journal / source
- Comptes Rendus Mathématique
- Volume
- 364
- Issue
- G2
- Pages
- 345–351
- Publication date
- 27 March 2026
- Language
- EN