Fourier-Mukai partners of Enriques and bielliptic surfaces in positive characteristic

TL;DR

This paper proves that certain algebraic surfaces in positive characteristic fields have no non-trivial Fourier-Mukai partners, clarifying their derived equivalence classifications in algebraic geometry.

Contribution

It establishes the uniqueness of Fourier-Mukai partners for twisted Enriques and untwisted bielliptic surfaces in specified positive characteristics.

Findings

Twisted Enriques surfaces have no non-trivial Fourier-Mukai partners in characteristic ≥3.

Untwisted bielliptic surfaces have no non-trivial Fourier-Mukai partners in characteristic ≥5.

Results extend understanding of derived categories of algebraic surfaces in positive characteristic.

Abstract

We prove that a twisted Enriques (respectively, untwisted bielliptic) surface over an algebraically closed field of positive characteristic at least 3 (respectively, at least 5) has no non-trivial Fourier-Mukai partners.