Fourier--Mukai partners of elliptic ruled surfaces over arbitrary characteristic fields

TL;DR

This paper generalizes the classification of Fourier--Mukai partners of elliptic ruled surfaces from complex fields to arbitrary characteristic fields, providing new insights and partial evidence for the Popa--Schnell conjecture.

Contribution

It extends the known results on Fourier--Mukai partners of elliptic ruled surfaces to all characteristic fields and offers partial support for the Popa--Schnell conjecture.

Findings

Explicit description of Fourier--Mukai partners over arbitrary characteristic fields

Partial evidence supporting the Popa--Schnell conjecture

Generalization of previous complex field results

Abstract

The first author explicitly describes the set of Fourier--Mukai partners of elliptic ruled surfaces over the complex number field in \cite{Ue17}. In this article, we generalize it over arbitrary characteristic fields. We also obtain a partial evidence of the Popa--Schnell conjecture in the proof.