Proof of Caldararu's conjecture. An appendix to a paper by Yoshioka

TL;DR

This paper proves Caldararu's conjecture by demonstrating that certain Hodge isometries between twisted K3 surfaces can be lifted to Fourier-Mukai equivalences, advancing understanding of derived categories and twisted sheaves.

Contribution

It establishes that orientation-preserving Hodge isometries between twisted K3 surfaces can be realized as Fourier-Mukai equivalences, confirming a key conjecture in the field.

Findings

Hodge isometries lift to Fourier-Mukai equivalences

Supports the conjecture for twisted K3 surfaces

Bridges Hodge theory and derived categories in algebraic geometry

Abstract

We show that any orientation preserving Hodge isometry between the Hodge structures of two K3 surfaces X and X' twisted by Brauer classes $\alpha$ resp. $\alpha'$ can be lifted to a Fourier-Mukai equivalence between the derived categories of $\alpha$ resp. $\alpha'$-twisted sheaves.