Donagi–Gao–Schulz reduction and derived-equivalence conjecture for Calabi-Yau threefolds

Let $\mathcal{X}_{1,3}$ and $\mathcal{X}_{3,1}$ denote the Calabi-Yau threefolds studied by Donagi, Gao, and Schulz, whose Betti cohomology has torsion at primes $p$ dividing that torsion. Donagi–Gao–Schulz reduction and derived-equivalence conjecture. The Calabi-Yau threefolds in the cited work can be constructed rigorously, and (generically) have good reduction at primes $p$ dividing the torsion in their Betti cohomology. Furthermore, the derived equivalences between these Calabi-Yau threefolds extend to characteristic $p$.

The conjecture is proposed as a route to showing that Hodge numbers are not derived invariants in positive characteristic; the source says it will be studied in future work and gives no resolution.